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Round 6
7 July 1964
| Cassidy (4½) |
(1-0) |
Byrne (3½) |
| Heidenfeld (4½) |
(1-0) |
Wilson (3½) |
| Lewis, W. (3) |
(½-½) |
O'Kane (3) |
| O'Riordan (3) |
(1-0) |
Ireton (3) |
| Cox (3) |
(½-½) |
Reilly (2½) |
| Lewis, E. W. (3) |
(1-0) |
O'Leary (2½) |
| Ballance (2½) |
(1-0) |
Coll (2½) |
| Cunnane (2) |
(0-1) |
O'Hare (2) |
| Ó Siochrú (1½) |
(1-0) |
Egan (2) |
| Stewart (1) |
(1-0) |
Doyle (1) |
| Collins (1½) |
1 |
Bye |
Scores after round 6
| Cassidy | 5½ |
| Heidenfeld | 5½ |
| Lewis, E. W. | 4 |
| O'Riordan | 4 |
| Ballance | 3½ |
| Byrne | 3½ |
| Cox | 3½ |
| Lewis, W. | 3½ |
| O'Kane | 3½ |
| Wilson | 3½ |
| Ireton | 3 |
| O'Hare | 3 |
| Reilly | 3 |
| Coll | 2½ |
| Collins | 2½ |
| O'Leary | 2½ |
| Ó Siochrú | 2½ |
| Cunnane | 2 |
| Egan | 2 |
| Stewart | 2 |
| Doyle | 1 |