During her career Nataliya Strunnikova competed at three major international tournaments. At the 1980 Olympics she won bronze in the medley relay, which she improved to silver at the 1981 Europeans. She also competed at the 1982 World Championships, but did not medal. Her best individual places at major international tournaments came at the 1980 Olympics, where she was sixth in the 100 free and seventh in the 200 free. Domestically, Strunnikova never won a Soviet title, but she won four silver medals (1981-82 100 freestyle, 1982 200 freestyle, and 1979 4x100 free relay) and bronze twice (1981 in 200/400 freestyle) at the Soviet championships.
Personal Best: 100 m freestyle – 56.59 (1981); 200 m freestyle – 2:02.34 (1982); 400 m freestyle – 4:24.03 (1981).