This paper presents efficient modeling technique using multi-dimensional method for prediction of free edge stresses in laminate plates. For the efficient modeling, the p-convergent transition element based on two-dimensional layer elements is proposed in order to connect discrete layer elements. The elements considered are on the basis of subparametric element concept. The results obtained by this proposed model are compared with those available in literatures. Especially, three-dimensional out-of-plane stresses in the interior and near the free edges are evaluated. The present models using the p-convergent transition element are demonstrated to be more practical and economical than previously p-version FEM using only single element type.