In this paper, a new three dimensional FEM model was elucidated on arch dam cracking analysis. Based on the least potential energy method, the stiffness of the interface between two types of mesh is coupled into the whole stiff matrix in this model. By this means, the FEM mesh of local area of arch dam can be easily changed from a coarse mesh to a fine mesh. By changing the density of mesh, the consideration of heterogeneity for the calculating elements is achieved by assigned to the elements random strength and elastic modulus according to a Weibull distribution. This model allows to densify the mesh of a local area and to trace the cracking of this area undertake damage criterion. By applying this new model, the mechanism of vertical cracks opening along the downstream surface of Shuanghe Arch Dam after two years of operation was briefly analyzed. The numerical result is basically agreed with the field investigation.