La Copa de Escocia 1959-60 fue la 75.ª edición de la competición más importante del fútbol escocés. El ganador de la Copa fue Rangers, quien derrotó a Kilmarnock en la final.
Primera ronda
| Local | Puntaje | Visitante |
|---|---|---|
| Aberdeen | 0-0 | Brechin City |
| Albion Rovers | 2-1 | Tarff Rovers |
| Berwick Rangers | 1-3 | Rangers |
| Clyde | 2-0 | Third Lanark |
| Dunfermline Athletic | 1-1 | St Johnstone |
| East Fife | 0-2 | Partick Thistle |
| Keith | 3-0 | Hamilton Academical |
| Kilmarnock | 5-0 | Stranraer |
| Greenock Morton | 0-1 | East Stirling |
| Queen of the South | 2-1 | Dumbarton |
| Queen’s Park | 2-0 | Raith Rovers |
| St Mirren | 15-0 | Glasgow University |
| Stenhousemuir | 2-0 | Rothes |
Repeticiones
| Local | Puntaje | Visitante |
|---|---|---|
| Brechin City | 3-6 | Aberdeen |
| St Johnstone | 1-4 | Dunfermline Athletic |
Segunda ronda
| Local | Puntaje | Visitante |
|---|---|---|
| Hibernian | 3-0 | Dundee |
| Hearts | 1-1 | Kilmarnock |
| Peebles Rovers | 1-6 | Ayr United |
| Aberdeen | 0-2 | Clyde |
| Alloa Athletic | 1-5 | Airdrieonians |
| Cowdenbeath | 1-0 | Falkirk |
| Dundee United | 2-2 | Partick Thistle |
| Dunfermline Athletic | 2-3 | Stenhousemuir |
| East Stirling | 2-2 | Inverness Caledonian |
| Elgin City | 5-1 | Forfar Athletic |
| Eyemouth United | 1-0 | Albion Rovers |
| Montrose | 2-2 | Queen’s Park |
| Motherwell | 6-0 | Keith |
| Rangers | 2-0 | Arbroath |
| St Mirren | 1-1 | Celtic |
| Stirling Albion | 3-3 | Queen of the South |
Repeticiones
| Local | Puntaje | Visitante |
|---|---|---|
| Queen’s Park | 1-1 | Montrose |
| Inverness Caledonian | 1-4 | East Stirling |
| Celtic | 4-4 | St Mirren |
| Kilmarnock | 2-1 | Hearts |
| Partick Thistle | 4-1 | Dundee United |
| Queen of the South | 5-1 | Stirling Albion |
Segundas repeticiones
| Local | Puntaje | Visitante |
|---|---|---|
| Queen’s Park | 2-1 | Montrose |
| Celtic | 5-2 | St Mirren |
Tercera ronda
| Local | Puntaje | Visitante |
|---|---|---|
| Clyde | 6-0 | Queen’s Park |
| East Stirling | 0-3 | Hibernian |
| Elgin City | 1-2 | Celtic |
| Ayr United | 4-2 | Airdrieonians |
| Eyemouth United | 3-0 | Cowdenbeath |
| Kilmarnock | 2-0 | Motherwell |
| Partick Thistle | 3-2 | Queen of the South |
| Stenhousemuir | 0-3 | Rangers |
Cuartos de final
| Local | Puntaje | Visitante |
|---|---|---|
| Ayr United | 0-2 | Clyde |
| Celtic | 2-0 | Partick Thistle |
| Eyemouth United | 1-2 | Kilmarnock |
| Rangers | 3-2 | Hibernian |
Semifinales
| 2 de abril de 1960 | Kilmarnock |
2-0
|
Clyde | Ibrox Stadium, Glasgow, | |
| Asistencia: 45.000 espectadores | |||||
| 2 de abril de 1960 | Kilmarnock |
1-1
|
Celtic | Hampden Park, Glasgow, | |
| Asistencia: 79.786 espectadores | |||||
Repeticiones
| 6 de abril de 1960 | Rangers |
4-1
|
Celtic | Hampden Park, Glasgow, | |
| Davie Wilson (2) Jimmy Millar (2) |
Neil Mochan | Asistencia: 70.977 espectadores | |||
Final
| 6 de abril de 1960 | Rangers |
2-0
|
Kilmarnock | Hampden Park, Glasgow, | |
| Jimmy Millar (2) | Asistencia: 108.017 espectadores | ||||
Equipos
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