Asle Sjåstad was an allround alpine skier. Between 1955 and 1960, he won eight Norwegian titles, four times in the downhill, three times in the giant slalom and once in the slalom. The alpine combination, maybe his best event, was not a Norwegian title event during these years. He did win the combined at the 1955 Holmenkollen Kandahar event, and placed 5th in the combined at the 1956 World Championships - held during the Olympics in Cortina, but not an Olympic event. It was his best international finish, also participating in the 1954 and 1958 World Championships and the Cortina Winter Games.