Elgh tried the traditional way in the 1970s by the single-seater formulas from the Formula Vee direction Formula 1 In the late 1970s he was regarded in Sweden as a great talent and was the successor to the short succession deceased by Swedish motorsport journalist Gunnar Nilsson and Ronnie Peterson seen. He was managed in the 1970s and 1980s by former racing driver Torsten Palm.
About the Formula Super Vee, Swedish and European, he came in 1977 to the British Formula 3 Championship. Not least because most Formula 1 teams had their factories in the UK and because of the large concentration of talented drivers was the British Championship as a stepping stone to Formula 1 1977 season denied the Swede for the Chevron Racing and was just behind Derek Daly ex aequo with Stephen South second in the championship
After the first race in 1977, he climbed in 1978 by the Formula 3 to the next higher class racing, Formula 2 and went to the team of Fred Opert at the start. Was later Opert Team Manager ATS Racing Team. The first season - emergency vehicle was a Chevron B42 - was quite successful for a Rockie. In Pau, he was with a gap of almost 20 seconds, Bruno Giacomelli, who drove a factory March 782, Second and finished the race at Rouen -les- Essarts and Hockenheim sixth. In the final standings of the championship, he placed himself as Gesamtelfter.
In 1979 he moved to Tiga Race Cars, who used a March 792 and won at the Autodromo di Pergusa his first Formula 2 race. His best year in the Formula 2 European Championship was the season of 1981. Already in the year before it was changed to Maurer Motorsport and had a disastrous first season without experiencing finish. In 1981 he won in Vallelunga, finished the race at Thruxton ( behind teammate Roberto Guerrero ) and the Eifel race on the Nürburgring Nordschleife ( behind Thierry Boutsen ) as well as the second race meeting at Spa as a third party. He took this position in the devaluation of the championship.
Despite these successes, the Swedes did not made the jump into Formula 1 World Championship, so he sought new challenges in Asia. In the early 1980s changed many European racers in the lucrative Japanese Monopostoserien. Elgh went there successfully in the Japanese Formula 2 and Formula 3000 Championship
Sports car racing
The mid - 1980 's began touring car and sports car career of Sweden. He was works driver at Dome and drove 1984 touring car race for the Volvo team of his compatriot Robert Kvist. Together with Ulf Granberg, he was second in the 500 - km race at Mugello, the twelfth championship round of the European Touring Car Championship in 1984.
By the end of his career in 1995 he was closely connected with Dome and the sports car Toyota team for which he was engaged almost continuously. Elgh was considered a strong development driver and a loyal team player who was also at times at Toyota, largely failed to materialize as successes. His first long-distance race he won in 1985; with partner Geoff Lees he triumphed at the 500 - km race at Suzuka, a race in the All Japan Sports Prototype Championship on a Dome 84C .. His last of four successes in the Japanese Sports Car Championship was the overall win in the 500 - km race from Sugo, 1991; again with Lee as a partner, this time in the Toyota 91C -V.
Ten times was the 24- hour race at Le Mans at the start. He made his debut in 1982; He achieved his best result in 1993 with the sixth overall.
Since the end of his racing career, he worked in Sweden as a TV commentator.