The purpose of this paper is to apply the boundary element method to predict the crack growth path. The quarter point element with traction singularity at the crack tip is applied to compact tension type specimens and two inclined slit problems under compression load. The maximum stress criterion which was originally derived for the crack initiation is extended to the analysis of the crack propagation. The predicted crack paths with 1/4 crack growth increment of initial crack length agree quite well with experimental results. It is found that the computed crack path of the boundary element analysis is not mainly affected by the crack increment length.