In this paper, interlaminar stresses resulting from static behavior of laminated plates, which were made from composite materials, were evaluated. To this end, out-of-plane stresses and displacements were considered as a primary variable. In addition, for the problem analysis, the boundary value problem method was expanded in order to form a first-order linear differential equations system which depended on the laminate thickness. This method could consider normal and transverse stresses and investigates a three-dimensional stress field near the free edge of the layers. In the proposed model, a laminated plate was placed on a simply supported boundary condition and under transverse loading. It was also assumed that the interlaminar transverse stresses, and displacements were continuous in layers' interfaces. The governing differential equations system was solved using Navier's approach and shooting method and, finally, the obtained results were compared with the results of other references. The results indicated good accuracy and high speed of the method used in analyzing stress field.