27th May 1995
| Final | Celtic | 1-0 | Airdrie United |
11th April 1995
| Semi Final Replay | Celtic | 3-1 | Hibernian |
8th April 1995
| Semi Final | Airdrie United | 1-0 | Heart of Midlothian |
7th April 1995
| Semi Final | Hibernian | 0-0 | Celtic |
12th March 1995
| 5th Round | Heart of Midlothian | 2-1 | Dundee United |
11th March 1995
| 5th Round | Raith Rovers | 1-4 | Airdrie United |
| 5th Round | Stenhousemuir | 0-4 | Hibernian |
10th March 1995
| 5th Round | Celtic | 1-0 | Kilmarnock |
20th February 1995
| 4th Round | Heart of Midlothian | 4-2 | Rangers |
18th February 1995
| 4th Round | Kilmarnock | 4-0 | East Fife |
| 4th Round | Airdrie United | 2-0 | Dunfermline Athletic |
| 4th Round | Celtic | 3-0 | Livingston |
| 4th Round | Dundee | 1-2 | Raith Rovers |
| 4th Round | Hibernian | 2-0 | Motherwell |
| 4th Round | 1-3 | Dundee United |
| 4th Round | Stenhousemuir | 2-0 | Aberdeen |
7th February 1995
| 3rd Round Replay | 3-3 | Livingston |
| 3rd Round Replay | Clyde | 1-5 | Dundee United |
| 3rd Round Replay | Heart of Midlothian | 2-1 |
| 3rd Round Replay | Stenhousemuir | 4-0 | St. Johnstone |
6th February 1995
| 3rd Round | Falkirk | 0-2 | Motherwell |
| 3rd Round | 1-3 | Rangers |
| 3rd Round | Livingston | 1-1 |
1st February 1995
| 3rd Round | 1-1 | Heart of Midlothian |
| 3rd Round | East Fife | 1-0 | Ross County |
| 3rd Round | Stirling Albion | 1-2 | Airdrie United |
31st January 1995
| 3rd Round Replay | Greenock Morton | 1-2 | Kilmarnock |
| 3rd Round | St. Johnstone | 1-1 | Stenhousemuir |
29th January 1995
| 3rd Round | Dundee | 2-1 | Partick Thistle |
28th January 1995
| 3rd Round | Aberdeen | 1-0 | Stranraer |
| 3rd Round | Celtic | 2-0 | St. Mirren |
| 3rd Round | Cove Rangers | 0-4 | Dunfermline Athletic |
| 3rd Round | Dundee United | 0-0 | Clyde |
| 3rd Round | 7-0 |
| 3rd Round | Kilmarnock | 0-0 | Greenock Morton |
| 3rd Round | Montrose | 0-2 | Hibernian |
| 3rd Round | Raith Rovers | 1-0 | Ayr United |
17th January 1995
| 2nd Round Replay | Greenock Morton | 2-1 | Queen's Park |
14th January 1995
| 2nd Round Replay | 3-1 |
| 2nd Round Replay | Montrose | 5-2 |
9th January 1995
| 2nd Round | Queen's Park | 2-2 | Greenock Morton |
7th January 1995
| 2nd Round | Alloa Athletic | 2-3 | Ross County |
| 2nd Round | 1-4 |
| 2nd Round | 6-2 |
| 2nd Round | Cove Rangers | 2-1 | Cowdenbeath |
| 2nd Round | Forfar Athletic | 0-1 | Livingston |
| 2nd Round | 2-6 | East Fife |
| 2nd Round | 2-2 |
| 2nd Round | Brechin City | 2-3 | Stirling Albion |
| 2nd Round | Stenhousemuir | 4-0 | Arbroath |
| 2nd Round | 0-0 | Montrose |
| 2nd Round | Queen of the South | 0-2 | Clyde |
26th December 1994
| 1st Round | Albion Rovers | 2-5 | Montrose |
19th December 1994
| 1st Round Replay | Stirling Albion | 3-0 | Dumbarton |
17th December 1994
| 1st Round | Stenhousemuir | 3-0 |
| 1st Round | Inverness Caledonian Thistle | 1-2 | Queen of the South |
| 1st Round | Dumbarton | 3-3 | Stirling Albion |