The men's Greco-Roman heavyweight competition at the 1956 Summer Olympics in Melbourne took place from 3 December to 6 December at the Royal Exhibition Building.

[1] Heavyweight was the heaviest category, including wrestlers weighing over 87 kilograms (191.8 lb).

[2] This Greco-Roman wrestling competition continued to use the "bad points" elimination system introduced at the 1928 Summer Olympics for Greco-Roman and at the 1932 Summer Olympics for freestyle wrestling, as modified in 1952 (adding medal rounds and making all losses worth three points—from 1936 to 1948 losses by split decision only cost two points).

At the end of each round, any wrestler with at least five points was eliminated.

This elimination continued until the medal rounds, which began when three wrestlers remained.