Bertil Rönnmark started competitive shooting at the age of 15 with his brother Lennart, who was to become a world class shooter and official. Bertil immediately showed talent and won a Mauser rifle as a prize in his second year competing, which he used for years. After his father’s early death the family moved to Stockholm, where he studied to be a pharmacist. He missed the qualifying, so he could not compete in the 1929 World Championships in Stockholm, but he studied the international shooters’ techniques. In order to be able to compete in more events, he also purchased a used free rifle made by Schulz & Larsen. Prior to the next World Championships held in 1931, he placed second in the selection, but was considered too inexperienced, and had to qualify in a dramatic shoot-out against 1912 gold medal winner Mauritz Eriksson.
Starting in 1931, Rönnmark won a total of six World titles – 1931 prone free rifle, individual and team; 1933 kneeling free rifle, military rifle, and team prone free rifle; and 1935 prone free rifle. He also won four silver and two bronze medals individually, and four silver and six bronze team medals between 1931-39. One of his world records, set in the kneeling free rifle, lasted for 22 years. After his gold medal in the 1932 Olympic small-bore rifle event, he competed again in the same event in 1936, placing eighth. A strong opponent of Nazi Germany, he terminated his international career after 1939. Later Rönnmark was on various shooting association boards. He worked as a pharmacist in Karlskrona, but later returned to Stockholm.