The men's triple jump competition at the 1968 Summer Olympics in Mexico City, Mexico took place on October 16–17. Thirty-four athletes from 24 nations competed. The maximum number of athletes per nation had been set at 3 since the 1930 Olympic Congress. The event was won by Viktor Saneyev of the Soviet Union, the first time the nation had won gold in the event. Saneyev began a decade of dominating the Olympic triple jump; he would win again in 1972 and 1976 as well as taking silver in 1980. Nelson Prudêncio's silver was Brazil's first medal in the event since 1956; Giuseppe Gentile's bronze was Italy's first men's triple jump medal ever.

Viktor Danilovich Saneyev was a Georgian triple jumper who competed internationally for the USSR. He won four Olympic medals – three golds and one silver (1980). Saneyev set the world record on three occasions. He was born in Sukhumi, Georgian SSR, trained in Sukhumi and Tbilisi, and died in Sydney.