| Game |
| Result | Moves |
Year |
Event/Locale | Opening |
| 1. A Kveinys vs E Vladimirov |
| 0-1 | 43 |
1988 |
URS Cup rapid | C61 Ruy Lopez, Bird's Defense |
| 2. A Kveinys vs Balashov |
| ½-½ | 22 |
1991 |
Miedzybrodzie | C92 Ruy Lopez, Closed |
| 3. A Kveinys vs Bronstein |
| 0-1 | 39 |
1994 |
It (open) | C95 Ruy Lopez, Closed, Breyer |
| 4. A Kveinys vs Blatny |
| 0-1 | 28 |
1994 |
Vienna open | C86 Ruy Lopez, Worrall Attack |
| 5. A Kveinys vs T Kilpi |
| 1-0 | 28 |
2001 |
Heart of Finland Open | C67 Ruy Lopez |
| 6. A Kveinys vs V Malisauskas |
| ½-½ | 10 |
2001 |
ch-LTU | C69 Ruy Lopez, Exchange, Gligoric Variation, 6.d4 |
| 7. A Kveinys vs M Grabarczyk |
| ½-½ | 22 |
2001 |
TCh-POL | C67 Ruy Lopez |
| 8. A Kveinys vs JM Dominiguez |
| 1-0 | 58 |
2002 |
Bled Olympiad | C60 Ruy Lopez |
| 9. A Kveinys vs V Harasta |
| 1-0 | 28 |
2003 |
Cappelle La Grande | C64 Ruy Lopez, Classical |
| 10. A Kveinys vs Beliavsky |
| ½-½ | 22 |
2003 |
EU-chT (Men) | C89 Ruy Lopez, Marshall |
| 11. A Kveinys vs N Eliet |
| ½-½ | 13 |
2004 |
20th Cappelle la Grande | C97 Ruy Lopez, Closed, Chigorin |
| 12. A Kveinys vs Kaidanov |
| ½-½ | 23 |
2004 |
36th Olympiad | C92 Ruy Lopez, Closed |
| 13. A Kveinys vs S Sulskis |
| 0-1 | 42 |
2005 |
Lithuanian Championship | C92 Ruy Lopez, Closed |
| 14. A Kveinys vs Pavasovic |
| ½-½ | 40 |
2006 |
37th Chess Olympiad | C95 Ruy Lopez, Closed, Breyer |