The finite element alternating method is a convenient and efficient method to analyze three-dimensional cracks embedded in an infinite or a finite body because the method has the property that the uncracked body and cracks can be modeled independently. In this paper the method was applied for fatigue crack growth simulation. A surface crack in a cylinder was considered as an initial crack and the crack configurations and stress intensity factors during the crack growth were obtained. In this paper the finite element alternating method proposed by Nikishkov, Park and Atluri was used after modification. In the method, as the required solution for a crack in an infinite body, the symmetric Galerkin boundary element method formulated by Li and Mear was used. And a crack was modeled as distribution of displacement discontinuities, and the governing equation was formulated as singularity-reduced integral equations.