Season 1959-60Rangers
 First Round
Jan30  2-1  Queen of the South v Dumbarton
Jan30  5-0  Kilmarnock v Stranraer
Jan30  1-3  Berwick Rangers v Rangers
Jan30  2-0  Clyde v Third Lanark
Jan30  2-0  Queen’s Park v Raith Rovers
Jan30  0-1  Greenock Morton v East Stirlingshire
Jan30  0-0  Aberdeen v Brechin City
Feb03  3-6  Brechin City v Aberdeen a.e.t. 3-3
Jan30  1-1  Dunfermline Athletic v St Johnstone
Feb03  1-4  St Johnstone v Dunfermline Athletic
Jan30  2-0  Stenhousemuir v Rothes
Jan30  2-1  Albion Rovers v Tarff Rovers
Jan30  3-0  Keith v Hamilton Academical
Jan30  0-2  East Fife v Partick Thistle
Jan30 15-0  St Mirren v Glasgow University
       bye  Airdrieonians, Arbroath, Ayr United,
            Celtic, Dundee, Heart of Midlothian,
            Hibernian, Motherwell, Stirling Albion,
            Alloa Athletic, Cowdenbeath, Dundee United,
            Falkirk, Forfar Athletic, Montrose,
            Inverness Caledonian, Elgin City, Eyemouth United,
            Peebles Rovers
 Second Round
Feb13  1-1  St Mirren v Celtic
Feb24  4-4  Celtic v St Mirren a.e.t. 3-3
Feb29  5-2  Celtic v St Mirren  at Celtic Park
Feb13  3-3  Stirling Albion v Queen of the South
Feb17  5-1  Queen of the South v Stirling Albion
Feb22  1-1  Heart of Midlothian v Kilmarnock
Feb24  2-1  Kilmarnock v Heart of Midlothian
Feb13  1-0  Eyemouth United v Albion Rovers
Feb13  2-2  Dundee United v Partick Thistle
Feb13  4-1  Partick Thistle v Dundee United
Feb13  2-0  Rangers v Arbroath
Feb13  5-1  Elgin City v Forfar Athletic
Feb13  2-3  Dunfermline Athletic v Stenhousemuir
Feb22  1-6  Peebles Rovers v Ayr United
Feb13  0-2  Aberdeen v Clyde
Feb29  3-0  Hibernian v Dundee
Feb13  2-2  East Stirlingshire v Inverness Caledonian
Feb27  1-4  Inverness Caledonian v East Stirlingshire
Feb13  2-2  Montrose v Queen’s Park
Feb29  1-1  Queen’s Park v Montrose a.e.t. 1-1
Mar01  1-2  Montrose v Queen’s Park  at Tynecastle Park a.e.t. 1-1
Feb13  6-0  Motherwell v Keith
Feb13  1-0  Cowdenbeath v Falkirk
Feb13  1-5  Alloa Athletic v Airdrieonians
 Third Round
Feb27  3-0  Eyemouth United v Cowdenbeath
Feb27  2-0  Kilmarnock v Motherwell
Mar05  6-0  Clyde v Queen’s Park
Mar05  1-2  Elgin City v Celtic
Feb27  0-3  Stenhousemuir v Rangers
Mar05  0-3  East Stirlingshire v Hibernian
Feb27  4-2  Ayr United v Airdrieonians
Feb27  3-2  Partick Thistle v Queen of the South
 Fourth Round
Mar12  0-2  Ayr United v Clyde
Mar12  1-2  Eyemouth United v Kilmarnock
Mar12  2-0  Celtic v Partick Thistle
Mar12  3-2  Rangers v Hibernian
 Semi-finals
Apr02  1-1  Rangers v Celtic  at Hampden Park
Apr06  4-1  Rangers v Celtic  at Hampden Park
Apr02  2-0  Kilmarnock v Clyde  at Ibrox Stadium
 Final
Apr23  2-0  Rangers v Kilmarnock  at Hampden Park