This is a question that has been debated for years.  It is in the first chapter of the book of Acts that we find the disciples choosing a replacement for Judas, the (false) disciple who betrayed the Lord and then killed himself.  It was the Apostle Peter who addressed this issue as we read in Acts 1:15-18, “And in those days Peter stood up in the midst of the disciples, and said, (the number of names together were about an hundred and twenty,) Men and brethren, this scripture must needs have been fulfilled, which the Holy Ghost by the mouth of David spake before concerning Judas, which was guide to them that took Jesus. For he was numbered with us, and had obtained part of this ministry. Now this man purchased a field with the reward of iniquity; and falling headlong, he burst asunder in the midst, and all his bowels gushed out.”  Using Psalm 41:9 to show that Judas’ betrayal of the Lord was prophesied, Peter then quoted Psalm 69:25, “Let their habitation be desolate; and let none dwell in their tents.”  He also quoted Psalm 109:8, “Let his days be few; and let another take his office.” I believe this was done under the guidance of the Holy Spirit, to show the Lord’s will and their responsibility to choose a successor for Judas. 

In verses 21-22, Peter pointed out the qualifications for one to be considered to replace Judas.  The disciples chose two men who met those qualifications, Joseph and Matthias.  They prayed and then used a principle used in the Old Testament to determine which one the Lord wanted to take Judas’ place.  They cast lots. (Read Leviticus 16:8, 1 Chronicles 24:5-7, Luke 1:9).  While Matthias was chosen to fill the ranks of the original apostles, we never read of apostolic succession in the Bible.  There are no apostles today because no one meets the qualifications pointed out in Acts 1:21-22.

We have addressed this issue before in Answers From the Book, but I wanted to go a little further in this answer to point out that the choosing of Matthias was scriptural and not choosing Paul at this point was not a mistake.  Paul considered himself to be an apostle because the Lord chose him.  He said in Galatians 1:1, “Paul, an apostle, (not of men, neither by man, but by Jesus Christ, and God the Father, who raised him from the dead;).”  He also said of himself in 1 Corinthians 15:8-9, “And last of all he was seen of me also, as of one born out of due time. For I am the least of the apostles, that am not meet to be called an apostle, because I persecuted the church of God.”  This birth (being born out of time) actually refers to a natural abortion which comes before its time.  It is usually sudden and unexpected and is also weak and frail. This refers to Paul’s sudden conversion on the way to Damascus to persecute the Lord’s people in Acts 9:1-9.  Because he was such an aggressive and active persecutor of the church, Paul considered himself to be unworthy to be called an apostle. 

Paul wrote in 1 Corinthians 9:1, “Am I not an apostle? am I not free? have I not seen Jesus Christ our Lord?”  This shows that Paul met one qualification to be an apostle as we just read in Acts 1:22 that one must be “a witness with us of his resurrection.”  It was on the Damascus Road experience that Paul actually saw and heard from the resurrected Christ.  However, he did not meet the other qualification that “Wherefore of these men which have companied with us all the time that the Lord Jesus went in and out among us, Beginning from the baptism of John, unto that same day that he was taken up from us, must one be ordained to be a witness with us of his resurrection.” (Verses 21-22).  Paul had no experience (that we know of) with the Lord Jesus as a man on the earth.  No, he knew the resurrected Christ.

It was a unique experience that the Lord called Paul to be an apostle.  Not once did Paul ever hint that he should have been the one chosen by the other apostles to take Judas’ place.  Some have commented that Matthias must not have been the one to take Judas’ place because he is not mentioned again in the scriptures.  However, notice that most of the apostles are never mentioned again after that day in Acts, chapter one.  We can take comfort in knowing that all these things happened according to the will and the leading of the Lord.  (CC)  (715.6)