1919-20 Scottish Cup
| Final | ||||||
| Albion Rovers | 2 | 3 | Kilmarnock | Sat 17 Apr 1920 | Details | |
| Semi Final | ||||||
| Kilmarnock | 3 | 2 | Greenock Morton | Sat 27 Mar 1920 | Details | |
| Albion Rovers | 1 | 1 | Rangers | Sat 27 Mar 1920 | Details | |
| Albion Rovers | 0 | 0 | Rangers | Wed 31 Mar 1920 | 1st Replay | Details |
| Albion Rovers | 2 | 0 | Rangers | Wed 07 Apr 1920 | 2nd Replay | Details |
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| 4th Round | ||||||
| Albion Rovers | 2 | 1 | Aberdeen | Sat 06 Mar 1920 | Details | |
| Armadale | 1 | 2 | Kilmarnock | Sat 06 Mar 1920 | Details | |
| Greenock Morton | 3 | 0 | Third Lanark | Sat 06 Mar 1920 | Details | |
| Rangers | 1 | 0 | Celtic | Sat 06 Mar 1920 | Details | |
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| 3rd Round | ||||||
| Raith Rovers | 2 | 2 | Greenock Morton | Sat 21 Feb 1920 | Details | |
| St Bernards Edinburgh | 1 | 1 | Albion Rovers | Sat 21 Feb 1920 | Details | |
| Rangers | 3 | 0 | Broxburn United | Sat 21 Feb 1920 | Details | |
| Lochgelly United | 0 | 3 | Third Lanark | Sat 21 Feb 1920 | Details | |
| Kilmarnock | 4 | 1 | Queen Of The South | Sat 21 Feb 1920 | Details | |
| Celtic | 2 | 0 | Partick Thistle | Sat 21 Feb 1920 | Details | |
| Ayr United | 1 | 1 | Armadale | Sat 21 Feb 1920 | Details | |
| Aberdeen | 1 | 0 | Hearts | Sat 21 Feb 1920 | Details | |
| Albion Rovers | 4 | 1 | St Bernards Edinburgh | Wed 25 Feb 1920 | 1st Replay | Details |
| Greenock Morton | 3 | 0 | Raith Rovers | Wed 25 Feb 1920 | 1st Replay | Details |
| Armadale | 1 | 0 | Ayr United | Sat 28 Feb 1920 | 1st Replay | Details |
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| 2nd Round | ||||||
| St Bernards Edinburgh | 2 | 0 | Bathgate | Sat 24 Jan 1920 | Details | |
| Armadale | 1 | 0 | Hibernian | Sat 07 Feb 1920 | Details | |
| Queen's Park | 3 | 0 | Vale Of Leithen | Sat 07 Feb 1920 | Details | |
| Partick Thistle | 5 | 0 | East Fife | Sat 07 Feb 1920 | Details | |
| Lochgelly United | 2 | 1 | Royal Albert | Sat 07 Feb 1920 | Details | |
| Hearts | 2 | 0 | Falkirk | Sat 07 Feb 1920 | Details | |
| Rangers | 5 | 0 | Arbroath | Sat 07 Feb 1920 | Details | |
| Third Lanark | 2 | 1 | Vale Of Leven | Sat 07 Feb 1920 | Details | |
| East Stirlingshire | 0 | 0 | Raith Rovers | Sat 07 Feb 1920 | Details | |
| Dundee | 1 | 3 | Celtic | Sat 07 Feb 1920 | Details | |
| Ayr United | 2 | 1 | St Mirren | Sat 07 Feb 1920 | Details | |
| Alloa Athletic | 0 | 2 | Kilmarnock | Sat 07 Feb 1920 | Details | |
| Aberdeen | 2 | 0 | Gala Fairydean | Sat 07 Feb 1920 | Details | |
| St Johnstone | 1 | 1 | Greenock Morton | Sat 07 Feb 1920 | Details | |
| Broxburn United | 1 | 0 | Queen Of The South | Sat 07 Feb 1920 | Details | |
| Greenock Morton | 5 | 3 | St Johnstone | Wed 11 Feb 1920 | 1st Replay | Details |
| Raith Rovers | 1 | 1 | East Stirlingshire | Wed 11 Feb 1920 | 1st Replay | Details |
| East Stirlingshire | 0 | 0 | Raith Rovers | Wed 18 Feb 1920 | 2nd Replay | Details |
| East Stirlingshire | 0 | 4 | Raith Rovers | Thu 19 Feb 1920 | 3rd Replay | Details |
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| 1st Round | ||||||
| Lochgelly United | 2 | 0 | Clachnacuddin | Sat 24 Jan 1920 | Details | |
| Greenock Morton | 4 | 0 | Forfar Athletic | Sat 24 Jan 1920 | Details | |
| Partick Thistle | 3 | 1 | Motherwell | Sat 24 Jan 1920 | Details | |
| Queen's Park | 2 | 0 | Hamilton | Sat 24 Jan 1920 | Details | |
| Rangers | 0 | 0 | Dumbarton | Sat 24 Jan 1920 | Details | |
| Royal Albert | 7 | 0 | Forres Mechanics | Sat 24 Jan 1920 | Details | |
| Stevenston United | 1 | 2 | St Mirren | Sat 24 Jan 1920 | Details | |
| Cowdenbeath | 0 | 1 | Aberdeen | Sat 24 Jan 1920 | Details | |
| Hearts | 5 | 1 | Nithsdale Wanderers | Sat 24 Jan 1920 | Details | |
| Third Lanark | 4 | 1 | Caledonian | Sat 24 Jan 1920 | Details | |
| Dumbarton Harp | 0 | 0 | Alloa Athletic | Sat 24 Jan 1920 | Details | |
| Armadale | 1 | 0 | Clyde | Sat 24 Jan 1920 | Details | |
| Albion Rovers | 0 | 0 | Dykehead | Sat 24 Jan 1920 | Details | |
| Dundee | 1 | 0 | Airdrieonians | Sat 24 Jan 1920 | Details | |
| East Fife | 4 | 0 | Arthurlie | Sat 24 Jan 1920 | Details | |
| East Stirlingshire | 6 | 0 | Thornhill | Sat 24 Jan 1920 | Details | |
| Galston | 0 | 0 | Hibernian | Sat 24 Jan 1920 | Details | |
| Rangers | 1 | 0 | Dumbarton | Tue 27 Jan 1920 | Details | |
| Dykehead | 1 | 2 | Albion Rovers | Sat 31 Jan 1920 | 1st Replay | Details |
| Hibernian | 2 | 1 | Galston | Sat 31 Jan 1920 | 1st Replay | Details |
| Alloa Athletic | 1 | 0 | Dumbarton Harp | Sat 31 Jan 1920 | 1st Replay | Details |
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