Meanwhile there was a solemn act to be performed on the part of the Church, which could not be postponed. The place of the fallen Judas must be filled up, that the elect number of the apostles might be complete. St. Peter, therefore, as Vicar of Christ, arose to announce the divine decree. That which the Holy Ghost had spoken by the mouth of David concerning Judas, he said, must be fulfilled. Of him it had been written, "His bishopric let another take." A choice, therefore, was to be made of one among those who had been their companions from the beginning, who could bear witness to the Resurrection of Jesus.
Two were named of equal merit, Joseph called Barsabas, and Matthias. Then, after praying to God, Who knows the hearts of all men, to show which of these He had chosen, they cast lots, and the lot fell upon Matthias, who was forthwith numbered with the apostles. It is recorded of the Saint, thus wonderfully elected to so high a vocation, that he was above all remarkable for his mortification of the flesh. It was thus that he made his election sure.
Click the link for more Facts and Information about the Patron Saint Matthias
Feast Day of Saint Matthias