| 1996 Summer Olympics | Artistic Gymnastics (Gymnastics) |  ISL |  |  | Rúnar Alexandersson |  | 
|  | Individual All-Around, Men
(Olympic) |  | 68 r1/2 |  |  |  | 
|  | Floor Exercise, Men
(Olympic) |  | 79 r1/1 |  |  |  | 
|  | Horse Vault, Men
(Olympic) |  | 89 r1/1 |  |  |  | 
|  | Parallel Bars, Men
(Olympic) |  | 92 r1/1 |  |  |  | 
|  | Horizontal Bar, Men
(Olympic) |  | 95 r1/1 |  |  |  | 
|  | Rings, Men
(Olympic) |  | =88 r1/1 |  |  |  | 
|  | Pommelled Horse, Men
(Olympic) |  | 75 r1/1 |  |  |  | 
| 2000 Summer Olympics | Artistic Gymnastics (Gymnastics) |  ISL |  |  | Rúnar Alexandersson |  | 
|  | Individual All-Around, Men
(Olympic) |  | 50 r1/2 |  |  |  | 
|  | Floor Exercise, Men
(Olympic) |  | 71 r1/1 |  |  |  | 
|  | Horse Vault, Men
(Olympic) |  | 79 r1/1 |  |  |  | 
|  | Parallel Bars, Men
(Olympic) |  | =35 r1/1 |  |  |  | 
|  | Horizontal Bar, Men
(Olympic) |  | =39 r1/1 |  |  |  | 
|  | Rings, Men
(Olympic) |  | 74 r1/1 |  |  |  | 
|  | Pommelled Horse, Men
(Olympic) |  | 79 r1/1 |  |  |  | 
| 2004 Summer Olympics | Artistic Gymnastics (Gymnastics) |  ISL |  |  | Rúnar Alexandersson |  | 
|  | Individual All-Around, Men
(Olympic) |  | 35 |  |  |  | 
|  | Floor Exercise, Men
(Olympic) |  | 74 r1/1 |  |  |  | 
|  | Horse Vault, Men
(Olympic) |  | 78 r1/1 |  |  |  | 
|  | Parallel Bars, Men
(Olympic) |  | 51 r1/1 |  |  |  | 
|  | Horizontal Bar, Men
(Olympic) |  | 65 r1/1 |  |  |  | 
|  | Rings, Men
(Olympic) |  | =58 r1/1 |  |  |  | 
|  | Pommelled Horse, Men
(Olympic) |  | 7 |  |  |  |