The 1981–82 Yugoslav Cup was the 34th season of the top football knockout competition in SFR Yugoslavia, the Yugoslav Cup (Serbo-Croatian: 'Kup Jugoslavije'), also known as the "Marshal Tito Cup" (Kup Maršala Tita), since its establishment in 1946.

The 1980–81 winners Velež failed to retain the trophy as they were knocked out in the first round by minnows Mogren. Dinamo Zagreb and the Belgrade-based Red Star, who finished as winners and runners-up in the 1981–82 Yugoslav First League, reached the tournament final. In the two-legged final Red Star won their 10th cup title after beating Dinamo 6–4 on aggregate. This was their first cup win since the 1970–71 edition.

Surprise of the tournament were second level side Galenika, who managed to reach the semi-finals, knocking out the remaining two of the Yugoslav "Big Four" clubs Partizan and Hajduk Split in the process. Fuelled by their prolific goalscorer Slobodan Santrač, Galenika also had a successful league season as they won the 1981–82 Second League Division East and won promotion to the 1982–83 Yugoslav First League.

The Yugoslav Cup was a tournament for which clubs from all tiers of the football pyramid were eligible to enter. In addition, amateur teams put together by individual Yugoslav People's Army garrisons and various factories and industrial plants were also encouraged to enter, which meant that each cup edition had thousands of teams in its initial stages. These teams would go through a number of qualifying rounds before reaching the first round proper, in which top-flight teams would enter.

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