For years, the Vatican has insisted that the bones of St. Peter were under the Basilica in a stone ossuary.
The relics of St. Peter, the first Pope, were found in a necropolis under St Peter's Basilica as it was excavated in the 1940s. Jesus' words in Matthew 16:18 state "And I tell you that you are Peter, and upon this rock I shall build my church and the gates of Hades shall not overcome it." Whether they really are Peter or not (the bones are said to have been of a "sturdily built man in his 60's - 70's consistent with the martyred saint"), it would certainly fulfill the words spoken.The
Catholic Herald said the bones had not been formally declared authentic
by a pope. However in 1968, Pope Paul VI said they had been “identified
in a way which we can hold to be convincing” after scientific tests
were carried out.
History / legend says that the bones had been found in the fourth
century and had been wrapped in rich cloth, remnants of which were
found. They were placed in a marble-lined niche in a wall in a monument
to St Peter that was erected at the same time and had lain undisturbed
since then. The cloth of purple interwoven with
gold-thread in which the bones were wrapped at that time confirms the
highest dignity then attributed to the remains.
According to news sources, for the first time ever, the relics will be put on display later this month and that Pope Francis will celebrate Mass that day.
Even though I'm not Catholic, I must say it would be exciting to be a part of this event...
There is an interesting and in-depth article about the tomb here...