The body of Jesus was laid in Joseph of Arimathea’s own tomb, a new one, in which no man had been laid, and this was cut out of a rock. As Jacob the patriarch was honorably buried by his son Joseph, so Christ, who is sometimes called Israel, was honorably buried by another Joseph, a "rich" man, which fulfilled the prophecy in Isaiah 53:9.
Christ was laid not in his own, but in "another’s" tomb, which is expressive of his humility. In his lifetime, Jesus had nowhere to lay down his head to sleep, and at his death had no tomb of his own to lay his dead body in. Thus, it denotes that what he did and suffered, and what was done to him, were not for himself but for others. He died not for his own sins, but for the sins of others, and he was buried, not so much for his own sake, but for others, that they and their sins might be buried with him.
It was a "new" tomb in which Christ was laid - he who makes all things new. He made the grave for his people quite a new and another thing to what it was. When he dwells in the hearts of men, old things pass away, and all become new.
In this tomb "was never man yet laid," something that was so ordered in providence that it might not be said that not he but another man rose from the dead or that he rose not by his own power, but by the touch of another body, as a man once rose by the touch of the body of Elisha (2 Kings 13:20). In addition, this tomb was "hewn out of the rock," as was sometimes the manner of rich men to do, to prepare such sepulchres while living for the greater security of their bodies when dead (Isaiah 22:16), and this prevented any such objection to be made to the resurrection of Christ that the apostles, through some subterraneous passages, got to the body of Christ and took it away. To all this may be added that at the door of this new tomb hewn out of a rock a great stone was rolled, and this stone sealed by the Jews themselves; so that no pretence could be made for a fraud or imposture in this affair.
Adapted from A Body of Doctrinal Divinity, Book 5, Chapter 3, by John Gill.