Season 1963-64Rangers
 First Round
Jan11  1-5  Stenhousemuir v Rangers
Jan11  2-1  Stranraer v Third Lanark
Jan11  3-0  Celtic v Eyemouth United
Jan11  0-0  Dundee United v St Mirren
Jan15  2-1  St Mirren v Dundee United
Jan11  4-0  Dumbarton v Raith Rovers
Jan11  5-2  Berwick Rangers v St Cuthbert Wanderers
Jan11  2-1  Kilmarnock v Gala Fairydean
Jan11  0-0  Greenock Morton v Cowdenbeath
Jan15  1-4  Cowdenbeath v Greenock Morton
Jan11  1-1  Stirling Albion v Brechin City
Jan15  5-1  Brechin City v Stirling Albion
Jan11  5-2  Aberdeen v Hibernian
Jan11  3-6  Forres Mechanics v Dundee
Jan11  1-1  Montrose v Alloa Athletic
Jan14  3-2  Alloa Athletic v Montrose
Jan11  3-2  Ayr United v Inverness Thistle
 Second Round
Jan25  2-2  Falkirk v Berwick Rangers
Jan29  1-5  Berwick Rangers v Falkirk
Jan25  1-3  Buckie Thistle v Ayr United
Jan25  9-0  Rangers v Duns
Jan25  1-1  Aberdeen v Queen’s Park
Jan29  1-2  Queen’s Park v Aberdeen a.e.t. 1-1
Jan25  1-3  Greenock Morton v Celtic
Jan25  0-1  East Fife v East Stirlingshire
Jan25  4-3  Albion Rovers v Arbroath
Jan25  2-9  Brechin City v Dundee
Jan25  4-1  Motherwell v Dumbarton
Jan25  0-3  Queen of the South v Heart of Midlothian
Jan25  2-0  St Mirren v Stranraer
Jan25  2-2  Clyde v Forfar Athletic
Jan29  3-2  Forfar Athletic v Clyde
Jan25  1-3  Alloa Athletic v Airdrieonians
Jan25  1-3  Hamilton Academical v Kilmarnock
Jan25  7-0  Dunfermline Athletic v Fraserburgh
Jan25  2-0  Partick Thistle v St Johnstone
 Third Round
Feb15  1-6  East Stirlingshire v Dunfermline Athletic
Feb15  6-1  Dundee v Forfar Athletic
Feb15  0-1  St Mirren v Falkirk
Feb15  3-3  Motherwell v Heart of Midlothian
Feb19  1-2  Heart of Midlothian v Motherwell
Feb15  3-0  Rangers v Partick Thistle
Feb15  2-0  Kilmarnock v Albion Rovers
Feb15  4-1  Celtic v Airdrieonians
Feb15  1-2  Aberdeen v Ayr United
 Fourth Round
Mar07  7-0  Dunfermline Athletic v Ayr United
Mar07  1-2  Falkirk v Kilmarnock
Mar07  1-1  Dundee v Motherwell
Mar11  2-4  Motherwell v Dundee
Mar07  2-0  Rangers v Celtic
 Semi-finals
Mar28  1-0  Rangers v Dunfermline Athletic  at Hampden Park
Mar28  0-4  Kilmarnock v Dundee  at Ibrox Park
 Final
Apr25  3-0  Rangers v Dundee  at Hampden Park