Joseph A. Fitzmyer, «Melchizedek in the MT, LXX, and the NT», Vol. 81 (2000) 63-69
Melchizedek is mentioned in the Hebrew Old Testament only in Gen 14,18-20 and Psalm 110,4. The details about this (originally Canaanite) priest-king in these passages were further read and understood in the Hellenistic and Roman periods of Jewish, and later Christian, history. This is seen in the translation or interpretation of the passages in the Septuagint, the writings of Flavius Josephus, the Epistle to the Hebrews, and in the Peshitta, where a process of allegorization was at work.
the king of Sodom asks Abram, hb ly nps\t) wqnyn) sb lk, give me the souls and take the acquired property for yourself; (4) in v. 22 Abram raises his hand to )lh) mrym), with no mention of an equivalent of hwhy, as already noted; (5) in Ps 110,4 the Peshitta renders the last part of the verse, )nt hw kwmr) l)lm bdmwth dmlkyzdq, you are a priest forever in the likeness of Melchizedek, which seems to be influenced by the interpretation of the peculiar phrase that is given in Heb 7,15, kata_ th_n o(moio/thta Melxise/dek 28.
In the Epistle to the Hebrews, Melchizedek becomes the type of Christ, who is designated there as a priest forever according to the order of Melchizedek (5,6; 6,20); he is thus the antitype of Melchizedek, depicted as in Ps 110,4. The main passage about Melchizedek in that Epistle (7,1-3) runs thus:
1 Now this Melchizedek, king of Salem, priest of the Most High God, met Abraham as he was returning from the defeat of the kings and blessed him; 2 to him Abraham allotted a tenth of everything. First of all, by the meaning of his name he is a king of righteousness; then he is also king of Salem, that is, king of peace. 3 He is without father or mother or genealogy and has neither beginning of days nor end of life, but resembling the Son of God he continues as a priest forever (Heb 7,1-3).
I have already commented on the phrase without father or mother or genealogy, but one should not fail to note how the name of Melchizedek and his city Salem are here allegorized. For his resemblance to the Son of God, we must await the Qumran material to explain it and the rest of v. 3.