An stress field near the crack line has been obtained for a near crack line field of a finite elastic-perfectly plastic medium containing a quasi-statically propagating crack subjected to pore water pressure. Strain energy density field in the vicinity of the crack tip is determined. According to the strain energy density theory, the minimum values of SED in the vicinity of the crack tip determine the potential initial crack growth direction. It is found from numerical results that the difference between the predicted angle from the elasto-perfectly plastic and the purely elastic material is very small.