In the process of analyzing crack growth with traditional finite element method, crack tip singularity is an urgent problem that must be faced with, and then the direction and length of the propagation are closely related to the mesh of model. In this paper, a model that is not thoroughly dependent on the mesh and can be used for analyzing problems of crack growth is set up. Because interaction integral method can relieve the effects of singularity to some extent, severe requirements for meshing caused by singularity can be avoided. Stress intensity factor at the crack tip is solved by interaction integral via finite element method, and direction of the propagation is determined by the maximum circumferential tensile stress theory. When cracks propagate, only the meshes of concerned areas are regenerated in order to obtain the final extension path in a relatively precise way. At last, several typical examples, including growth of mode-I crack, cracks with a hole plate and cracks subjected to compression, are compared with references. Reliability of the method in this paper is verified and applicability in many damaged patterns is shown as well.