A finite element calculation has been utilized to investigate the plane symmetric double receding contact problem for a rigid stamp and two elastic layers. Elastic layers have different elastic constants and heights. The external load is applied to the upper elastic layer by means of a rigid stamp and the lower elastic layer is bonded to a rigid support. The external load is applied to the upper elastic layer by means of a rigid stamp and the lower elastic layer is bonded to a rigid support. The problem is solved under the assumptions that the contact between two elastic layers, and between the rigid stamp and the upper elastic layer are frictionless, the effect of gravity force is neglected. Numerical simulations are realized by the world wide code ANYS software based on FEM. The model provides dimensionless expressions for the contact areas and contact pressures. This paper presents comparison with numerical solutions and analytical solutions. Calculated contact areas and contact pressures may be used for the optimal design of layer system as well as together with analytical solutions.