1959–60 Yugoslav Cup

The 1959–60 Yugoslav Cup was the 13th season of the top football knockout competition in SFR Yugoslavia, the Yugoslav Cup, also known as the "Marshal Tito Cup" (Kup Maršala Tita), since its establishment in 1946.

Calendar
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 could have several thousands of teams in its preliminary stages. These teams would play through a number of qualifying rounds before reaching the first round proper, in which they would be paired with top-flight teams.

The cup final was played on 26 May, traditionally scheduled to coincide with Youth Day celebrated on 25 May, a national holiday in Yugoslavia which also doubled as the official commemoration of Josip Broz Tito's birthday.

First round
In the following tables winning teams are marked in bold; teams from outside top level are marked in italic script.