| FAI Cup | |
| Year: | 1935–36 |
| Country: | Republic of Ireland |
| Dates: | 1 January – 19 April 1936 |
| Num Teams: | 16 |
| Defending Champions: | Bohemian |
| Winners: | Shamrock Rovers |
| Second: | Cork |
| Matches: | 22 |
| Goals: | 101 |
| Prev Season: | 1934-35 |
| Next Season: | 1936-37 |
The FAI Cup 1935 - 36 was the fifteenth edition of Ireland's premier cup competition, The Football Association of Ireland Challenge Cup or FAI Cup. The tournament began on 1 January 1936 and concluded on 19 April with the final held at Dalymount Park, Dublin. An official attendance of 30,946 people watched Shamrock Rovers claim their seventh title by defeating Cork.
| Tie no | Home team | Score | Away team | Date | |
|---|---|---|---|---|---|
| 1 | GSR | 1-4 | Reds United | 1 January 1936 | |
| 2 | Bohemians | 7-0 | Waterford | 11 January 1936 | |
| 3 | Cork | 2-2 | Bray Unknowns | 12 January 1936 | |
| replay | Bray Unknowns | 1-6 | Cork | 15 January 1936 | |
| 4 | Dolphin | 1-0 | Drumcondra | 12 January 1936 | |
| refix | Dolphin | 3-6 | Drumcondra | 16 January 1936 | |
| 5 | Dundalk | 7-1 | B&I | 12 January 1936 | |
| 6 | Hospitals Trust | 2-5 | Sligo Rovers | 12 January 1936 | |
| 7 | Shamrock Rovers | 1-1 | St James's Gate | 12 January 1936 | |
| replay | St James's Gate | 1-2 | Shamrock Rovers | 15 January 1936 | |
| 8 | Tramore Rookies | 1-5 | Brideville | 12 January 1936 |
| Tie no | Home team | Score | Away team | Date | |
|---|---|---|---|---|---|
| 1 | Bohemians | 1-1 | Cork | 8 February 1936 | |
| replay | Cork | 3-2 | Bohemians | 19 February 1936 | |
| 2 | Dundalk | 2-1 | Reds United | 8 February 1936 | |
| 3 | Drumcondra | 1-1 | Sligo Rovers | 9 February 1936 | |
| replay | Sligo Rovers | 1-1 | Drumcondra | 12 February 1936 | |
| replay(2) | Drumcondra | 3-2 | Sligo Rovers | 19 February 1936 | |
| 4 | Shamrock Rovers | 5-1 | Brideville | 9 February 1936 |
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A. From 1923 to 1936, the FAI Cup was known as the Free State Cup.
B. Attendances were calculated using gate receipts which limited their accuracy as a large proportion of people, particularly children, attended football matches in Ireland throughout the 20th century for free by a number of means.
C. Fixture abandoned due to encroachment of spectators. Re-Fixture played on 16 January.