14th May 1988
| Final | Celtic | 2-1 | Dundee United |
20th April 1988
| Semi Final 2nd Replay | Aberdeen | 0-1 | Dundee United |
13th April 1988
| Semi Final Replay | Aberdeen | 1-1 | Dundee United |
9th April 1988
| Semi Final | Celtic | 2-1 | Heart of Midlothian |
| Semi Final | Aberdeen | 0-0 | Dundee United |
28th March 1988
| 5th Round 2nd Replay | Dundee | 0-3 | Dundee United |
15th March 1988
| 5th Round Replay | Dundee United | 2-2 | Dundee |
12th March 1988
| 5th Round | Partick Thistle | 0-3 | Celtic |
| 5th Round | Heart of Midlothian | 3-0 | Dunfermline Athletic |
| 5th Round | Dundee | 0-0 | Dundee United |
| 5th Round | Aberdeen | 5-0 | Clyde |
23rd February 1988
| 4th Round Replay | Partick Thistle | 4-1 |
| 4th Round Replay | Hibernian | 0-1 | Celtic |
21st February 1988
| 4th Round | Celtic | 0-0 | Hibernian |
20th February 1988
| 4th Round | Heart of Midlothian | 2-0 | Greenock Morton |
| 4th Round | 0-2 | Aberdeen |
| 4th Round | 2-3 | Clyde |
| 4th Round | Dunfermline Athletic | 2-0 | Rangers |
| 4th Round | Dundee | 2-0 | Motherwell |
| 4th Round | 2-2 | Partick Thistle |
| 4th Round | Airdrie United | 0-2 | Dundee United |
10th February 1988
| 3rd Round Replay | Rangers | 4-1 | Raith Rovers |
| 3rd Round Replay | Partick Thistle | 3-0 | Forfar Athletic |
8th February 1988
| 3rd Round | Raith Rovers | 0-0 | Rangers |
3rd February 1988
| 3rd Round Replay | Kilmarnock | 1-3 | Motherwell |
| 3rd Round | Forfar Athletic | 1-1 | Partick Thistle |
| 3rd Round Replay | Cowdenbeath | 0-1 | Clyde |
| 3rd Round Replay | Brechin City | 0-3 | Dundee |
| 3rd Round Replay | Ayr United | 0-2 | Dunfermline Athletic |
2nd February 1988
| 3rd Round Replay | Hibernian | 3-0 | Dumbarton |
31st January 1988
| 3rd Round | 2-0 |
30th January 1988
| 3rd Round | St. Mirren | 0-3 |
| 3rd Round | St. Johnstone | 0-1 | Aberdeen |
| 3rd Round | Queen of the South | 1-2 | Greenock Morton |
| 3rd Round | Motherwell | 0-0 | Kilmarnock |
| 3rd Round | 3-5 |
| 3rd Round | Falkirk | 1-3 | Heart of Midlothian |
| 3rd Round | East Fife | 1-2 | Airdrie United |
| 3rd Round | Dunfermline Athletic | 1-1 | Ayr United |
| 3rd Round | Dundee | 0-0 | Brechin City |
| 3rd Round | Dumbarton | 0-0 | Hibernian |
| 3rd Round | Clyde | 0-0 | Cowdenbeath |
| 3rd Round | Celtic | 1-0 | Stranraer |
| 3rd Round | Arbroath | 0-7 | Dundee United |
18th January 1988
| 2nd Round 2nd Replay | Stenhousemuir | 0-1 | Arbroath |
12th January 1988
| 2nd Round Replay | Arbroath | 1-1 | Stenhousemuir |
10th January 1988
| 2nd Round | Alloa Athletic | 0-1 | Cowdenbeath |
9th January 1988
| 2nd Round | Stranraer | 6-2 |
| 2nd Round | Stenhousemuir | 1-1 | Arbroath |
| 2nd Round | Queen's Park | 2-3 | Ayr United |
| 2nd Round | 3-0 |
| 2nd Round | 2-5 | St. Johnstone |
| 2nd Round | 2-3 |
| 2nd Round | 0-1 | Brechin City |
21st December 1987
| 1st Round Replay | 2-1 |
12th December 1987
| 1st Round | 1-1 |
8th December 1987
| 1st Round Replay | St. Johnstone | 2-0 | Albion Rovers |
5th December 1987
| 1st Round | 2-3 | Brechin City |
| 1st Round | 0-6 | Stranraer |
| 1st Round | Stirling Albion | 1-2 | Cowdenbeath |
| 1st Round | Montrose | 0-2 | Ayr United |
| 1st Round | Albion Rovers | 1-1 | St. Johnstone |