The defendant, Nicholas Basey, appeals his conviction of aggravated rape on the ground that there was insufficient evidence to support the jury’s conclusion that he committed the rape by a joint enterprise. See G. L. c. 265, § 22. For the following reasons, the defendant’s arguments fail and we affirm.

On November 18, 2008, a group of men congregated in a wooded area in the D.W. Fields Park in Brockton to drink alcohol. *279Among the men present were the victim, James Smith,1 and his roommates, Willie and Carlos, as well as the defendant and, later, Keith Magner and a man named Russ. At some point, Smith’s roommates left him in the woods with the other men, after which point he has no recollection of what occurred that evening. The next morning, Smith awoke with pain radiating from his face, feet, and “butt.” He had no shoes on, no pants, was covered in blood from head to toe, and was still bleeding from the side of his head. Unable to walk, he crawled out of the woods and was eventually taken to the Boston Medical Center where he was intubated and treated for his injuries. In addition to having very low blood pressure and having suffered hypothermia, Smith had abrasions and contusions all over his body and was bleeding from his rectum. He was taken to an operating room where the injuries to his rectum were treated.

The treating trauma surgeon testified at trial that the injury to Smith’s rectum was approximately four to five inches past his anal opening, and was an injury consistent with having been sodomized with a stick or other similar object. Smith also had abrasions to his inner thighs and bruising to the lining of his rectum. The doctor performed a colostomy to treat Smith’s injuries, a procedure which diverted stool from the lower part of Smith’s rectum and which was in place for approximately four to five months.

The doctor also testified that Smith had suffered substantial injuries to his head, including a broken nose and numerous lacerations to his forehead and his ears, his left ear having been almost completely severed from his head. Smith spent his first night in the hospital in the intensive care unit where he was sedated and intubated, and spent approximately two weeks thereafter in the hospital in recovery.

Keith Magner, who was also present in the woods that evening, testified at trial under a grant of immunity. He testified that after Smith’s friends had left, the only people remaining were himself, the defendant, Smith, and a man named Russ. Magner testified that the defendant approached Smith, who had been sleeping in a chair near a fire they had built in the woods, and *280punched him in the face until he fell from his chair. Magner testified that once Smith was on the ground, the defendant continued to punch him, put him face down on a rock, and stated, “I wanna fuck him,” and pulled down Smith’s pants. Magner then saw the defendant pick up a stick, and later saw the defendant pull the stick out of Smith’s anus. He testified that he could smell feces.

Magner then testified that the defendant threw the stick in the woods and threatened Magner not to tell anybody, at which point the defendant retrieved another stick and began beating Smith with it. Hearing people coming, the defendant grabbed Magner and told him that they needed to leave, so they ran together until Magner passed out. Magner testified that he was later brought to a friend’s house and was revived when water was poured over his head. Magner was arrested the next day and charged, though he denied ever striking Smith.

The defendant was also arrested and interviewed by the police. The interview was videotaped and a redacted portion was played for the jury. The defendant initially claimed that Smith had fallen on a large rock, which caused his injuries. When told that Smith’s pants were missing, the defendant stated, “[Y]ou trying to say somebody raped him?” although the subject of rape had not yet been discussed. Eventually the defendant admitted that he punched Smith several times, but told police that Magner also participated in the beating. He also stated that Magner stayed behind for approximately two minutes after the assault. When asked about the stick, the defendant responded that he had seen Magner with it, but that he had not touched it. The defendant was then left alone in the interview room, at which point he stated aloud, “Got my DNA,[2] fucking bullshit .... I’m fucking going to jail for this thing.”

Both the defendant’s clothes and shoes and Magner’s sneakers tested positive for human blood, which matched Smith’s DNA profile. The blood on Magner’s sneakers was consistent with a “downward directionality,” which indicated that it was from a drop of blood traveling downwards as it hit the sneakers.

For the defense, Jay Jones testified that he was in the woods *281on the evening of November 18, 2008, and he observed Magner and Smith swinging at each other. He testified that at some point he saw Magner hit Smith with a stick and later, when Magner left the woods, Magner told Jones, “I think I killed [Smith], . . . I hit him. I knocked him down. ... Do you think I’m going to go to jail?”

The jury were instructed at the close of evidence that they could find the defendant guilty of aggravated rape under one of two theories: that the rape resulted in serious bodily injury or that it was committed in the process of a joint venture. At that point an instruction on joint venture was given, to which the defendant objected.

The defendant was convicted of aggravated rape, the jury specifying aggravation by joint enterprise and rejecting aggravation by serious bodily injury. The defendant was acquitted of assault and battery by means of a dangerous weapon (stick) but convicted of assault and battery causing serious bodily injury. The defendant appeals on the basis that there was insufficient evidence to support the jury’s finding that he committed the rape as part of a joint enterprise.3

Our analysis is controlled in essential part by the Supreme Judicial Court’s decision in Commonwealth v. Casale, 381 Mass. 167 (1980). In that case, convictions of murder on a joint venture theory were upheld against a sufficiency of the evidence challenge where each defendant was one of a group (defendants’ group) that had expressed hostility in person toward the victim’s group.4 Id. at 168-170. The defendants’ group went across the street to a playground from which five shots were fired, killing the victim. There was no evidence as to which member of the defendants’ group fired the shots, nor any other evidence about the mental state of the defendants.

This case is similar. The evidence would have supported a conclusion by the jury that both Magner and the defendant as*282saulted the victim. It would also have supported a conclusion that Magner and the defendant were together in the woods the entire time of the incident, including the time during which the rape was committed. There is in fact even evidence in this case, unlike Casale, that would have supported the conclusion that either Magner or the defendant was the “principal,” that is, that either one of them actually physically committed the rape here.5

The evidence of the defendant and Magner acting jointly is at least as strong as the evidence found to support conviction on a joint venture theory in Casale. The defendant relies on the fact that both the defendant and Magner testified that it was the other person who had committed the rape, and that neither of them testified that they engaged in a joint enterprise. This type of testimony, in which two people present during the commission of a crime each blame the other, is not exceptional. The jury were free to reject both versions of events, which were, of course, self-serving. The evidence that remained was sufficient under Casale to support the verdict.

Although the defendant has not argued that there is any substantive difference in what must be proven to demonstrate joint venture and joint enterprise, at oral argument, in reliance on Commonwealth v. Medeiros, 456 Mass. 52 (2010), he argued that evidence that might be sufficient to support conviction of a crime on a joint venture theory might nonetheless be insufficient to support a jury finding of rape by joint enterprise. See G. L. c. 265, § 22(a). We reject the argument.

To be sure, rape by joint enterprise, the Supreme Judicial Court has explained, “is a crime that requires ‘the united act of two or more individuals to constitute an offence in either.’ ” Medeiros, 456 Mass. at 60, quoting from Commonwealth v. Slate, 11 Gray 60, 63 (1858). “[T]he Commonwealth must prove beyond a reasonable doubt that the rape was committed by at least two people.” Ibid. And the Supreme Judicial Court has explained that “[cjommission of rape by ‘joint enterprise’ *283where the ‘joint enterprise’ is an element of the crime is distinct from general liability as a joint venturer.” Id. at 60 n.10. But the difference is that the former is a crime that requires two people as an element of the offense, while the latter type of liability attaches to crimes that can be committed in many ways.6 The relevance of this is not that proof beyond a reasonable doubt of joint enterprise requires something more in the way of evidence than proof beyond a reasonable doubt of joint venture. Cf., e.g., Commonwealth v. Jansen, 459 Mass. 21, 28 n.20 (2011) (essentially equating the substantive elements of liability for rape on a theory of joint venture with those of aggravated rape on a theory of joint enterprise). It means only that inconsistent verdicts that might be permissible when two individuals are charged with a single crime on a joint venture theory are not permissible when two individuals are charged with rape aggravated by commission as a joint enterprise. Indeed, that is the holding of Medeiros. See Commonwealth v. Fluellen, 456 Mass. 517, 523 n.7 (2010) (declining to extend the inconsistent verdict theory of Medeiros to joint venture liability because, despite the fact that “evidence of the participation of multiple individuals in a crime is required to receive a joint venture instruction, that instruction has no bearing on the elements of the underlying substantive crime”). The question we ask when sufficiency of the evidence is at issue is the same in each context.

The defendant also raises an argument about the sufficiency of the evidence presented to the grand jury on the charge of *284“aggravated rape by reason of joint venture.” The defendant did not file a pretrial motion to dismiss pursuant to Commonwealth v. McCarthy, 385 Mass. 160, 161-164 (1982); nor did the defendant make any attempt to obtain the grand jury minutes or the written or recorded statements of witnesses who testified before the grand jury — items to which he was entitled under Mass.R.Crim.P. 14(a)(1)(A)(ii), as amended, 444 Mass. 1501 (2005). Because we do not have the minutes of the grand jury before us or the statements of the testifying witnesses, the appellate record is insufficient and we are unable to assess this claim.

Judgments affirmed.