Abstract: The element-free Galerkin method for predicting fatigue crack propagation path and structure lifetime under mixed mode loading is presented in this paper. This method is used in order to allow for crack growth without remeshing and the degradation in accuracy with crack propagation in simulation process is overcome successfully. Using the results of a EFG method analysis, the J-integral and stress intensity factors K_I and K_Ⅱ are computed. The crack deflection angle Φ₀ is determined by the criterion of maximum stress in tangential direction. An assumed crack increment Δa, for each computing cycle delivers an estimation for the number of load cycles, ΔN, using the strain energy density factor theory. Numerical results for a CGS-04-specimen made of Ti-6Al-4V are presented and compared with experimental data.