On both occasions their exit from the tournament was marred by misfortune and controversy.
In England they finished their semi-final with West Germany down to nine men.
Sabo had already limped off injured when Chislenko, Russia's influential winger, got himself sent off for kicking out at an opponent.
The Germans took advantage and scored twice. Russia got one back but it was not to be and Eusebio's Portugal also proved too strong in the third-place play-off.
Four years on Russia's place in the last four was denied by a highly-controversial goal against Uruguay.
The South Americans scored in the last minute of extra-time, when a cross which appeared to have been delivered from beyond the touchline, set up a goal by Esparrago which was allowed to stand.
Success since then for Russia, or as the Soviet Union in 1986 and 1990, has been far harder to come by.
Salenko's five-goal burst in 1994 came far too late and this time Russia will be seeking a success story of far greater substance.