| Yugoslav Football Cup | |
| Year: | 1959–60 |
| Other Titles: | 13th Marshal Tito Cup |
| Country: | Yugoslavia |
| Dates: | 2 December 1959 – 26 May 1960 |
| Num Teams: | 32 |
| Defending Champions: | Red Star Belgrade |
| Winners: | Dinamo Zagreb (2nd title) |
| Second: | Partizan |
| Matches: | 31 |
| Prev Season: | 1958–59 |
| Next Season: | 1960–61 |
The 1959–60 Yugoslav Cup was the 13th season of the top football knockout competition in SFR Yugoslavia, the Yugoslav Cup (Kup Jugoslavije), also known as the "Marshal Tito Cup" (Kup Maršala Tita), since its establishment in 1946.
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.
| width=200 | Round ! | width=60 | Legs ! | width=130 | Date ! | width=100 | Fixtures ! | width=100 | Clubs |
|---|---|---|---|---|---|---|---|---|---|
| First round (round of 32) | Single | 2 December 1959 | 16 | 32 → 16 | |||||
| Second round (round of 16) | Single | 13 December 1959 | 8 | 16 → 8 | |||||
| Quarter-finals | Single | 28 December 1959 | 4 | 8 → 4 | |||||
| Semi-finals | Single | 6 March 1960 | 2 | 4 → 2 | |||||
| Final | Single | 26 May 1960 | 1 | 2 → 1 | |||||
In the following tables winning teams are marked in bold; teams from outside top level are marked in italic script.
| width=40 | Tie no | width=150 | Home team | width=80 | Score | width=150 | Away team |
|---|---|---|---|---|---|---|---|
| 1 | Borac Banja Luka | 0–2 | Hajduk Split | ||||
| 2 | Bosna Visoko | 0–3 | OFK Belgrade | ||||
| 3 | Branik Maribor | 0–3 | Vojvodina | ||||
| 4 | Elektrostroj Zagreb | 4–0 | RNK Split | ||||
| 5 | Napredak Kruševac | 0–2 | Radnički Kragujevac | ||||
| 6 | Novi Sad | 2–0 | Radnički Sombor | ||||
| 7 | Pobeda Prilep | 0–1 | Velež | ||||
| 8 | Radnički Belgrade | 1–1 (3–4 p) | Budućnost Titograd | ||||
| 9 | Radnički Niš | 3–1 | Sarajevo | ||||
| 10 | Red Star | 2–2 (5–6 p) | Partizan | ||||
| 11 | Sloga Vukovar | 2–6 | Lokomotiva Zagreb | ||||
| 12 | Spartak Subotica | 5–1 | Rijeka | ||||
| 13 | Srem | 1–2 (a.e.t.) | Dinamo Zagreb | ||||
| 14 | Sutjeska Nikšić | 2–0 | Vardar | ||||
| 15 | Trešnjevka | 2–1 | Sloboda Tuzla | ||||
| 16 | Željezničar Sarajevo | 1–0 | Proleter Osijek |
| width=40 | Tie no | width=150 | Home team | width=80 | Score | width=150 | Away team |
|---|---|---|---|---|---|---|---|
| 1 | Budućnost Titograd | 0–1 | Željezničar Sarajevo | ||||
| 2 | Dinamo Zagreb | 3–2 (a.e.t.) | Trešnjevka | ||||
| 3 | Elektrostroj Zagreb | 4–1 | Sutjeska Nikšić | ||||
| 4 | Hajduk Split | 4–2 | Novi Sad | ||||
| 5 | OFK Belgrade | 1–0 | Lokomotiva Zagreb | ||||
| 6 | Spartak Subotica | 3–4 (a.e.t.) | Partizan | ||||
| 7 | Velež | 8–1 | Radnički Kragujevac | ||||
| 8 | Vojvodina | 7–2 | Radnički Niš |
| width=40 | Tie no | width=150 | Home team | width=80 | Score | width=150 | Away team |
|---|---|---|---|---|---|---|---|
| 1 | Dinamo Zagreb | 2–1 | Vojvodina | ||||
| 2 | Hajduk Split | 2–1 | Elektrostroj Zagreb | ||||
| 3 | Partizan | 2–1 | Željezničar Sarajevo | ||||
| 4 | Velež | 1–0 | OFK Belgrade |
| width=40 | Tie no | width=150 | Home team | width=80 | Score | width=150 | Away team |
|---|---|---|---|---|---|---|---|
| 1 | Dinamo Zagreb | 2–1 | Hajduk Split | ||||
| 2 | Velež | 2–3 | Partizan |
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