Abstract: A systematic study is made on those formula by which the critical fatigue strength or fatigue life of a structure under asymmetric loading can be estimated. The prerequisites for some famous formula such as Goodman formula, Soderberg formula and Gerber formula are discussed, and a unified formula for predicting the critical fatigue strength or fatigue life of a structure under asymmetric loading is established The new formula has two important features: l) it is valid to any shape of failure surface; 2) its parameters can be correctly estimated from any type of experimental data of fatigue.