How did Saint Peter die?

Answer 1

The Catholic Encyclopedia states: (with references to historical documents)

Concerning the manner of Peter's death, we possess a tradition - attested to by Tertullian at the end of the second century and by Origen (in Eusebius, Church History II.1)-that he suffered crucifixion. Origen says: "Peter was crucified at Rome with his head downwards, as he himself had desired to suffer".

I was unable to find any historical document that stated "Pope Anicetus" stated Peter was beheaded.

The discussion between Polycarp and Anicetus concerned the establishment of the date of the celebration of Easter and had nothing what-so-ever to do with the martyrdom of Peter. This argument about the date for the celebration of Easter is the only surviving, document from the reign on Anicetus. Anicetus said he spoke with the authority of Peter and Easter should be celebrated on the Sunday following Passover. Polycarp said he spoke with the authority of John and Easter should be celebrated on the specific date of the resurrection, no matter what day of the week. This according to writings of Irenaeus.

Answer 2

For nearly 2000 years the Church has held to the tradition that Peter died in Rome by crucifixion upside down under Emperor Nero.
Many biblical historians today have concluded that the Acts of the Apostles was completed while both Peter and Paul were still alive but nearing the ends of their lives. Had the Acts been written towards the end of the first century it surely would have mentioned their deaths as well as the destruction of Jerusalem in AD 70. Peter was put on the cross and, as he wished, upside down . He died in Rome.

Answer 3

The Bible never mentions Simon Peter's death. Acts of the Apostles mentions the imprisonment and miraculous release of Peter, but does not say anything about his subsequent death, even though the book was written around the end of the century, long after Peter would have died.

However, the mid-second century pope Anicetus (156-166) said that Peter was beheaded by Nero in Rome. The reason for this claim was that he had became locked in a conflict with Polycarp of Smyrna. Polycarp had tried to win the argument by insisting that he spoke with the authority of the apostle John. In response, Anicetus told of Peter's beheading and said that he spoke with the authority of Peter. Then in the third century, the Church Father Origen changed the story somewhat, saying that Peter, condemned to crucifixion, felt himself unworthy to be crucified the same way as his Lord, and so chose crucifixion upside down.

In fact, we do not know how or where Simon Peter died.