It's logical to question how it could be the third day, when Christ was in the grave for a full three days and three nights as He had promised in Matthew 12:39-40. In Luke 24, the two disciples referred to Sunday as being the third day since "all these things" (Luke 24:14) happened. There were other things the Jews and Romans did after Christ was buried. Notice what Matthew included about their actions:
"On the next day, which followed the Day of Preparation, the chief priests and Pharisees gathered together to Pilate, saying, 'Sir, we remember, while He was still alive, how that deceiver said, "After three days I will rise." Therefore command that the tomb be made secure until the third day, lest His disciples come by night and steal Him away, and say to the people, "He has risen from the dead." So the last deception will be worse than the first.' Pilate said to them, 'You have a guard; go your way, make it as secure as you know how.' So they went and made the tomb secure, sealing the stone and setting the guard" (Matthew 27:62-66).
Christ had already been buried nearly one whole day when these things were done.
The last things the Romans and Jewish leaders did were to seal the tomb and place soldiers on guard around it. Christ died on Wednesday afternoon. So the tomb was sealed on Thursday, the day following that Day of Preparation. Apparently the disciples were including these events in their reference to the things that had taken place. Counting from the securing of the tomb and the setting of the guard, Sunday would have been the "third day" since "all these things" happened.
For more information about the death and resurrection of Jesus Christ, please read our booklet, Jesus Christ: The Real Story.