Season 1975-76Rangers
 First Round
Dec13  0-0  Albion Rovers v Hawick Royal Albert
Dec18  0-3  Hawick Royal Albert v Albion Rovers
Dec13  0-1  Elgin City v Forres Mechanics
Dec13  0-2  Peterhead v Raith Rovers
Dec13  1-1  Brechin City v Berwick Rangers
Dec20  3-3  Berwick Rangers v Brechin City a.e.t. 3-3
Dec22  1-0  Brechin City v Berwick Rangers  at Easter Road
Dec13  0-5  East Stirlingshire v Alloa Athletic
Dec13  1-0  Stranraer v Queen’s Park
 Second Round
Jan10  1-2  Forres Mechanics v Alloa Athletic
Jan10  1-1  Albion Rovers v Glasgow University
Jan14  0-1  Glasgow University v Albion Rovers
Jan10  2-0  Cowdenbeath v Selkirk
Jan10  2-2  Stenhousemuir v Brechin City
Jan14  0-1  Brechin City v Stenhousemuir
Jan10  3-1  Raith Rovers v Clydebank
Jan10  2-3  Stranraer v Keith
Jan10  2-1  Forfar Athletic v Meadowbank Thistle
Jan10  4-0  Stirling Albion v Civil Service Strollers
 Third Round
Jan24  3-2  Hibernian v Dunfermline Athletic
Jan24  2-1  Stirling Albion v Forfar Athletic
Jan24  4-0  Dundee United v Hamilton Academical
Jan24  3-0  Cowdenbeath v St Mirren
Jan24  3-0  Rangers v East Fife
Jan24  1-3  Greenock Morton v Montrose
Jan24  2-0  Dumbarton v Keith
Jan24  1-2  Albion Rovers v Partick Thistle
Jan24  1-0  Raith Rovers v Arbroath
Jan24  4-2  Ayr United v Airdrieonians
Jan24  0-4  Alloa Athletic v Aberdeen
Jan24  2-2  Heart of Midlothian v Clyde
Jan28  0-1  Clyde v Heart of Midlothian
Jan24  1-1  Stenhousemuir v Kilmarnock
Jan28  1-0  Kilmarnock v Stenhousemuir
Jan24  3-2  Motherwell v Celtic
Jan24  1-2  Dundee v Falkirk
Jan24  3-2  Queen of the South v St Johnstone
 Fourth Round
Feb14  3-0  Heart of Midlothian v Stirling Albion
Feb14  0-0  Partick Thistle v Dumbarton
Feb25  1-0  Dumbarton v Partick Thistle
Feb14  3-1  Kilmarnock v Falkirk
Feb14  0-2  Cowdenbeath v Motherwell
Feb14  4-1  Rangers v Aberdeen
Feb14  2-1  Montrose v Raith Rovers
Feb14  2-2  Ayr United v Queen of the South
Feb18  5-4  Queen of the South v Ayr United a.e.t. 4-4
Feb14  1-1  Hibernian v Dundee United
Feb25  0-2  Dundee United v Hibernian
 Fifth Round
Mar06  2-2  Motherwell v Hibernian
Mar10  1-1  Hibernian v Motherwell a.e.t. 1-1
Mar15  2-1  Motherwell v Hibernian  at Ibrox Park
Mar06  2-2  Montrose v Heart of Midlothian
Mar09  2-2  Heart of Midlothian v Montrose a.e.t. 2-2
Mar16  1-2  Montrose v Heart of Midlothian  at Muirton Park a.e.t. 1-1
Mar06  2-1  Dumbarton v Kilmarnock
Mar06  0-5  Queen of the South v Rangers
 Semi-finals
Mar31  3-2  Rangers v Motherwell  at Hampden Park
Apr03  0-0  Heart of Midlothian v Dumbarton  at Hampden Park
Apr14  3-0  Heart of Midlothian v Dumbarton  at Hampden Park
 Final
May01  3-1  Rangers v Heart of Midlothian  at Hampden Park