 Šimůnek finished 8th in the Nordic combined and 23rd in ski jumping at the 1932 Winter Olympics in Lake Placid.Four years later he finished 5th in both the 4 x 10 km cross-country and the Nordic combined, and 11th in the 18 km cross-country event at the 1936 Winter Olympics in Garmisch-Partenkirchen.He competed also in the 1948 Winter Olympics held in St. Moritz.