There are three common empirical expressions used for the fatigue curves, which are power function, exponential function and three-parameter power function expression, respectively. The mathematical difference between the former two and the latter is whether there exists the constant term S0 in the equations. The S0 can be calculated to determine whether the two-paprameter expression or three-parameter expression should be used. If the two-parameter expression should be used, the power function and exponential function expressions can be compared to determine which one is the optimum one. Finally, the method has been validated by several groups of fatigue data.