The 010, like all Tyrrells before it was powered by the Ford-Cosworth DFV V8 engine and made its competition debut in the third race of the season in South Africa.

The 010s were driven by Frenchman Jean-Pierre Jarier and Irishman Derek Daly, with New Zealander Mike Thackwell driving a third car at the last two races of the season.

Alboreto who was making his F1 debut and the first of an eventual 194 starts from 215 attempts in Formula One in a career which would see 5 wins, 2 pole positions, 23 podium finishes and runner up in the 1985 World Drivers' Championship while driving for Ferrari.

The last race for the 010 was the 1981 Austrian Grand Prix where Alboreto qualified 22nd and retired after 40 laps with gearbox failure.

This car would be the first Tyrrell since the 004 (which was only raced three times by the main team in 1972 and twice more by South African Eddie Keizan in a non-works effort for the 1973 and 1974 South African Grand Prix races) which failed to get a single podium finish and since neither the 009 at the beginning of 1980 (after having obtained a few third-place finishes during 1979) nor the 011 at the end of 1981 (which would go on to get a victory with Michele Alboreto in the 1982 Caesers Palace Grand Prix at Las Vegas) allowed Tyrrell a top-three finish during the seasons in question, 1980 and 1981 would be the first and second full seasons from a Tyrrell-built Tyrrell entry without a podium (Tyrrell cars were podiumless in 1970 but were only raced in the last three events while Jackie Stewart won earlier in that season in a Tyrrell-entered March at Jarama, Spain).