Tore Eriksson was part of the successful Swedish biathlon relay team that won bronze medals at the 1967 World Championships in Altenberg in East Germany and – running second leg – at the 1968 Olympic Winter Games. His Olympics relay teammates were Lars-Göran Arwidson, Olle Petrusson and Holmfrid Olsson. Eriksson lived his whole life in his native Transtrand, where he was very active in community affairs and with the mountain rescue team. Many sources also attribute to him the bronze medal in the first relay event at the Biathlon World Championships 1966 in Garmisch-Partenkirchen, but that was his compatriot and 1964 Olympian Sten Eriksson.