From: 'St. Peter's Basilica - A Virtual Tour' by Our Sunday Visitor
Also to be admired is the very elegant crafting of the capitals crowning the columns at the sides of the altars, in fluted porphyry, yellow and ancient yellow granite. The last of these flank the central altarpiece while two identical ones flank the corresponding altar dedicated to St. Processo and St. Martiniano in the opposite right hand transept.

The decoration of this central altar was extremely problematic and the final result is far from satisfactory. In 1822, a mosaic copy of the famous "Crucifixion of St. Peter" hanging in the Vatican Pinacoteca, a work by Guido Reni in which Caravaggio's influence on him was strongest, was placed here as a replacement for an altarpiece by A. Ciampelli showing the above mentioned saints. This mosaic has, however, recently been moved over the altar on the left. At the sides of the altar are two round mosaics by V. Camuccini, representing "St. Simon" and "St. Jude."

From: 'The Mosaics of Saint Peter's by Frank DiFrederico
Originally on this altar was a painting of 1630 by Agostino Ciampelli representing saints Simon and Jude. In February 1814 it was replaced by the mosaic after Guido Reni's Crucifixion of Saint Peter, which previously had been in the sacristy. The dedication of the altar to saints Simon and Jude was then memorialized by two mosaic ovals representing the saints on the walls on the sides of the altar... Crucifixion of Saint Peter was in turn replaced by Saint Joseph, which had been commissioned by Pope John XXIII. The painting by Achille Funi was presented to the mosaic studio in 1961. The mosaic by Virgilio Cassio, Odoardo Anselmi, Silvio Secchi, Fabrizio Parsi, and Giulio Perificati was placed on the altar in 1963.