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Stresses distribution between the interfaces of the materials is critical for structures like thin film layers, organic/inorganic light emitting diode layers and various kinds of modern optical-electronics components with stacking materials properties. The classical Aleck's model ( 1949 ) can be considered as a very simple and a practical method to analyze these kinds of structures. In order to deal with it, the integration scheme is used to solve the displacement equations with zero displacements on the clamped edge including the clamped corner. The condition of zero traction is imposed at all of the grid points on the free surface except for the clamped corner of layers. The results show a stress singularity at the clamped corner. This agrees with an existing finite element solution performed on a very fine grid. By contrast, the known Kantorovich solution for Aleck problem from Blech and Kantor (1984) did not predict such stress singularity. As remarked by Blech and Kantor, the Kantorovich solution posed difficulties in convergence in the immediate vicinity of the clamped corner, thus is questionable to apply the results for the layer structures through this model.