Uncini debuted in professional racing with Laverda in the 750cc class. He later switched to Ducati and was able to win some Italian championships. Uncini competed first races in the world championship in 1976 with Yamaha in the classes up to 250 and up to 350 cm³. In his Grand Prix debut at the Grand Prix of Nations in Mugello , Uncini did not make it into the points in the 250 cc, but took second place in the 350 cc behind Johnny Cecotto . After another podium in Barcelona, he finished ninth in the final championship of the 350 class with just three races. The following year he won his first Grand Prix on a Harley-Davidson in the 250cc class in Imola . After another victory in Brno and several podium places, he finished second behind Mario Lega at the end of the season . Uncini moved back to Yamaha in 1978 because of disputes with his teammate Walter Villa and ended this season with three podium finishes in the 250 cc class in eighth place in the World Championship. In the 350s he was able to get a second place behind Kork Ballington on the Salzburgring .
In the 1979 season Uncini founded a private team in the class up to 500 cm³ with a used Suzuki . In the first race of the season he took fourth and in Rijeka behind Kenny Roberts sr. and Virginio Ferrari took third place. He finished the world championship as the best private driver in fifth. In the 1980 season , with a second place as the best result in only eight races held due to three cancellations - again as the best private driver - he achieved fourth place in the World Championship.
The 1981 season was affected by injuries, but after Marco Lucchinelli's move from Suzuki to Honda, Uncini was still offered a works contract with Suzuki for 1982 . Uncini seized the chance and took the world title with five wins ahead of Graeme Crosby and Freddie Spencer .
In 1983 , Uncini was seriously injured and comatose in a collision with Wayne Gardner at Assen , but made a full recovery and retired from his active career after the 1985 season . Today Uncini works as the IRTA safety officer for the motorcycle world championship.
Italy