G-theta method with appropriate virtual crack extension (theta field) is proposed for the accurate evaluation of energy release rate along a crack edge which is non-orthogonal to the free surface. This method is implemented in the framework of finite element procedure as well as extended finite element one. This numerical procedure is then applied to investigate the corner singularities in cracked plates. The superposition of numerical solution to asymptotic solution within the boundary layer of crack front allows showing the dependence of vertex singularity to plate thickness.