Rolf Storsveen was one of the strongest Norwegian biathletes, especially in the first half of the 1980s. The athlete from Sørskogbygda Idrettslag first took part in the Biathlon World Championships in Minsk in 1982 and won the silver medal there with Eirik Kvalfoss , Kjell Søbak and Odd Lirhus as the final runner in the Norwegian relay behind the representation of the GDR. The 1984 Winter Olympics in Sarajevo were also quite successful , with Storsveen finishing sixth in the individual and second behind the Soviet relay with Lirhus, Kvalfoss and Søbak. In 1985 the Norwegian took part again in a World Championship in Ruhpolding , where he just missed another medal in fourth place in the relay race.
National was Storsveen in 1981 in Bardufoss individual champion. In 1984 the runner-up behind Kvalfoss was added again in Vossestrand . He was also runner-up in sprint races behind Sigleif Johansen in 1981 . He achieved further successes especially with the relay, for which he represented the Østerdal region until 1984 and for Hedmark since 1985. In 1980, 1981, 1983, 1984 and 1985 he was champion, in 1982 and 1987 runner-up and in 1991 third.