| Rangers (Glasgow) FC v Clyde 07/11/1959 | View match | |
| Motherwell FC v Clyde 14/11/1959 | View match | |
| Clyde v Arbroath FC 21/11/1959 | View match | |
| Clyde v Heart Of Midlothian (Hearts) 28/11/1959 | View match | |
| Third Lanark v Clyde 05/12/1959 | View match | |
| Dunfermline Athletic v Clyde 12/12/1959 | View match | |
| Clyde v Kilmarnock FC 19/12/1959 | View match | |
| Clyde v Ayr United FC 26/12/1959 | View match | |
| Partick Thistle FC v Clyde 01/01/1960 | View match | |
| Clyde v Stirling Albion FC 02/01/1960 | View match | |
| Dundee v Clyde 09/01/1960 | View match | |
| Clyde v Celtic (Glasgow) FC 16/01/1960 | View match |