| Matches: 1954 – 1955 | Match Pictures: 1954-55 | Scottish Cup |
Fifth Round
| Airdrieonians | 4 – 3 | Forfar Athletic |
| Alloa Athletic | 2 – 4 | Celtic |
| Arbroath | 0 – 4 | St. Johnstone |
| Buckie Thistle | 2 – 0 | Inverness Thistle |
| Clyde | 3 – 0 | Albion Rovers |
| Dunfermline Athletic | 4 – 2 | Partick Thistle |
| East Fife | 1 – 2 | Kilmarnock |
| Falkirk | 4 – 0 | Stenhousemuir |
| Forres Mechanics | 3 – 4 | Motherwell |
| Hamilton Academical | 2 – 1 | St. Mirren |
| Hearts | 5 – 0 | Hibernian |
| Inverness Caledonian | 1 – 1 | Ayr United |
| Greenock Morton | 1 – 3 | Raith Rovers |
| Rangers | 0 – 0 | Dundee |
| Stirling Albion | 0 – 6 | Aberdeen |
| Third Lanark | 2 – 1 | Queen of the South |
Replays Fifth Round
| Ayr United | 2 – 4 | Inverness Caledonian |
| Dundee | 0 – 1 | Rangers |
Sixth Round
| Aberdeen | 2 – 1 | Rangers |
| Airdrieonians | 7 – 0 | Dunfermline Athletic |
| Buckie Thistle | 0 – 6 | Hearts |
| Clyde | 3 – 1 | Raith Rovers |
| Inverness Caledonian | 0 – 7 | Falkirk |
| Kilmarnock | 1 – 1 | Celtic |
| St. Johnstone | 0 – 1 | Hamilton Academical |
| Third Lanark | 1 – 3 | Motherwell |
Replays Sixth Round
| Celtic | 1 – 0 | Kilmarnock |
Quarter Finals
| Airdrieonians | 4 – 1 | Motherwell |
| Celtic | 2 – 1 | Hamilton Academical |
| Clyde | 5 – 0 | Falkirk |
| Hearts | 1 – 1 | Aberdeen |
Quarter Final replay
| Aberdeen | 2 – 0 | Hearts |
Semi Finals
| Clyde | 2 – 2 | Aberdeen |
| Celtic | 2 – 2 | Airdrieonians |
Semi Final replays
| Clyde | 1 – 0 | Aberdeen |
| Celtic | 2 – 0 | Airdrieonians |
Final
| Clyde | 1 – 1 | Celtic |
Final Replay
| Clyde | 1 – 0 | Celtic |
Cup Winners: Clyde.