de Rham was also one of the best mountaineers in Switzerland. As a member of the Independent High Mountain Group of Lausanne since 1944, he opened several difficult routes, some of them in the Valais Alps (such as the south ridge of the Stockhorn from Baltschieder) and Vaud Alps (such as L'Argentine and Pacheu). In 1944 he wrote a complete climbing guidebook of the Miroir d'Argentine, where he climbed routes until 1980. According John Milnor, in 1933 de Rham encountered on one of his hikes James Alexander and Hassler Whitney, who were climbing together near the Weisshorn in Valais; this meeting was the beginning of a more than 40-year friendship between Whitney and de Rham.