USSR Cup 1990/91, 1/64 finals |
 | 14.04.1990 | | Volgar (Astrakhan) | – | FK Kutaisi (Kutaisi) | | +:- |
| |
USSR Cup 1989/90, 1/64 finals |
| 02.05.1989 | | Sokol (Saratov) | – | Torpedo (Kutaisi) | | 6:3 (3:1) |
| Saratov |
USSR Cup 1988/89, Quarterfinal |
| 29.04.1989 | | Dynamo (Kiev) | – | Torpedo (Kutaisi) | | 3:0 (3:0) |
 | Kiev |
USSR Cup 1987/88, 1/32 finals |
| 25.06.1987 | | Krasnaya Presnya (Moscow) | – | Torpedo (Kutaisi) | | 1:0 (1:0) |
| Moscow |
USSR Cup 1985/86, 1/16 finals |
| 14.08.1985 | | Torpedo (Kutaisi) | – | Daugava (Riga) | | 0:2 (0:0) |
| Kutaisi |
USSR Cup 1984/85, 1/32 finals |
| 10.08.1984 | | SKA (Khabarovsk) | – | Torpedo (Kutaisi) | | 6:1 (2:1) |
| Khabarovsk |
USSR Cup 1984, 1/16 finals |
| 22.02.1984 | | Shakhtyor (Donetsk) | – | Torpedo (Kutaisi) | | 2:0 (1:0) |
| Sochi |
USSR Cup 1982, Zone 6 |
| 28.02.1982 | | Lokomotiv (Moscow) | – | Torpedo (Kutaisi) | | 3:2 (1:1) |
| Khosta |
USSR Cup 1982, Zone 6 |
| 25.02.1982 | | Kuban (Krasnodar) | – | Torpedo (Kutaisi) | | 1:0 (0:0) |
| Sochi |
USSR Cup 1981, Zone 3 |
| 23.02.1981 | | Zenit (Leningrad) | – | Torpedo (Kutaisi) | | 8:1 (6:0) |
| Leningrad |
USSR Cup 1980, Zone 4 |
| 07.03.1980 | | Kairat (Alma-Ata) | – | Torpedo (Kutaisi) | | 3:0 |
| |
USSR Cup 1980, Zone 4 |
| 04.03.1980 | | Dynamo (Tbilisi) | – | Torpedo (Kutaisi) | | 3:1 (0:0) |
| Tbilisi |
USSR Cup 1980, Zone 4 |
| 01.03.1980 | | SKA (Odessa) | – | Torpedo (Kutaisi) | | 2:1 (0:0) |
| Tbilisi |
USSR Cup 1979, Zone 1 |
| 09.03.1979 | | Dynamo (Tbilisi) | – | Torpedo (Kutaisi) | | 3:0 (1:0) |
| Tbilisi |
USSR Cup 1978, 1/32 finals |
| 11.03.1978 | | Uralmash (Sverdlovsk) | – | Torpedo (Kutaisi) | | 2:0 aet,
pen. 5:3 |
| Fergana |
USSR Cup 1977, 1/32 finals |
| 27.03.1977 | | Torpedo (Kutaisi) | – | Metallist (Kharkov) | | 0:1 (0:1) |
| Kutaisi |
USSR Cup 1976, 1/16 finals |
| 27.03.1976 | | Torpedo (Kutaisi) | – | CSKA (Moscow) | | 0:1 (0:1) |
| Kutaisi |
USSR Cup 1975, 1/32 finals |
| 16.03.1975 | | Neftchi (Baku) | – | Torpedo (Kutaisi) | | 1:0 (0:0) |
| Bakı |
USSR Cup 1974, 1/32 finals |
| 10.03.1974 | | Shinnik (Yaroslavl) | – | Torpedo (Kutaisi) | | 1:0 (0:0) |
| Adler |
USSR Cup 1973, 1/16 finals |
| 01.04.1973 | | CSKA (Moscow) | – | Torpedo (Kutaisi) | | 2:1 (0:1) |
| Simferopol |
USSR Cup 1973, 1/16 finals |
| 16.03.1973 | | Torpedo (Kutaisi) | – | CSKA (Moscow) | | 0:3 (0:2) |
| Kutaisi |
USSR Cup 1972, 1/16 finals |
| 05.03.1972 | | Torpedo (Kutaisi) | – | Torpedo (Moscow) | | 0:1 (0:1) |
| Sochi |
USSR Cup 1972, 1/16 finals |
| 26.02.1972 | | Torpedo (Moscow) | – | Torpedo (Kutaisi) | | 2:1 (0:0) |
| Sochi |
USSR Cup 1971, 1/16 finals |
| 19.03.1971 | | Torpedo (Kutaisi) | – | CSKA (Moscow) | | 1:2 (1:1) |
| Sochi |
USSR Cup 1971, 1/16 finals |
| 15.03.1971 | | CSKA (Moscow) | – | Torpedo (Kutaisi) | | 1:0 (1:0) |
| Sochi |
USSR Cup 1969, 1/16 finals |
| 21.05.1969 | | Sudostroitel (Nikolaev) | – | Torpedo (Kutaisi) | | 2:1 aet
(1:1, 1:1) |
| Mykolaiv |
USSR Cup 1967/68, 1/16 finals |
| 28.06.1968 | | Zarya (Lugansk) | – | Torpedo (Kutaisi) | | 3:1 (0:0) |
| Lugansk |
USSR Cup 1966/67, 1/16 finals |
| 19.05.1967 | | Lokomotiv (Moscow) | – | Torpedo (Kutaisi) | | 4:0 (1:0) |
| Moscow |
USSR Cup 1965/66, 1/16 finals |
| 07.08.1966 | | Dynamo (Leningrad) | – | Torpedo (Kutaisi) | | 1:0 (0:0) |
| Leningrad |
USSR Cup 1965, 1/16 finals |
| 05.05.1965 | | Torpedo (Kutaisi) | – | CSKA (Moscow) | | 1:3 (1:2) |
| Kutaisi |
USSR Cup 1964, 1/16 finals |
| 08.06.1964 | | SKF (Sevastopol) | – | Torpedo (Kutaisi) | | 1:0 (0:0) |
| Sevastopol |
USSR Cup 1963, 1/16 finals |
| 17.06.1963 | | SKA (Khabarovsk) | – | Torpedo (Kutaisi) | | 1:0 aet * |
| Khabarovsk |
USSR Cup 1962, 1/16 finals |
| 19.06.1962 | | Dynamo (Tbilisi) | – | Torpedo (Kutaisi) | | 4:3 (2:1) |
| Tbilisi |
USSR Cup 1961, 1/32 finals |
| 15.07.1961 | | Torpedo (Kutaisi) | – | Kolhospnyk (Cherkassy) | | 0:1 |
| Kutaisi |
USSR Cup 1959/60, Zone 3, quarterfinal |
| 24.06.1959 | | Spartak (Nalchik) | – | Torpedo (Kutaisi) | | 5:2 (2:1) * |
| Nalchik |
USSR Cup 1958, Zone 4, semifinal |
| 18.07.1958 | | Terek (Groznyi) | – | Lokomotiv (Kutaisi) | | 2:0 |
| Grozny |
USSR Cup 1957, Zone 3, semifinal |
| 08.05.1957 | | Lokomotiv (Chelyabinsk) | – | Lokomotiv (Kutaisi) | | 1:0 (1:0) |
| Chelyabinsk |
USSR Cup 1955, Zone 4, 1/128 finals |
| 06.07.1955 | | Dynamo (Kutaisi) | – | ODO (Tbilisi) | | 1:2 (1:0) |
| Kutaisi |
USSR Cup 1953, 1/64 finals |
| 08.09.1953 | | Spartak (Tashkent) | – | Dynamo (Kutaisi) | | 4:2 (2:2) * |
| Toshkent Spartak Stadium |
USSR Cup 1949, 1/32 finals |
| 06.10.1949 | | Inkaras (Kaunas) | – | Dynamo (Kutaisi) | | 4:2 * |
| Kaunas |
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