Fatigue crack initiation lives of round cylindrical notch specimen were investigated. Firstly, local strain approximation methods, such as the modified incremental Neubers rule and the modified incremental Glinkas equivalent strain energy density(ESED) rule, were used to get multiaxial stress and strain state components at the notch tip. Based on the history of local stress and strain, multiaxial fatigue models were used to obtain fatigue crack initiation lives. Because the solution of Neubers rule and Glinkas ESED rule make the upper and lower bound of local strain approximations, fatigue crack initiation lives are expected to place between life predictions by two local strain approximations. Experimental data were compared with the fatigue crack initiation life prediction results.