In this study, a two dimensional model of receding contact problem has been analyzed using finite element method (FEM) based software ANSYS and ABAQUS. For this aim finite element modeling of elastic layer and two homogeneous, isotropic and symmetrical elastic quarter planes pressed by means of a rigid circular punch has been presented. Mass forces and friction are neglected in the solution. Since the problem is examined for the plane state, the thickness along the z-axis direction is taken as a unit. In order to check the accuracy of the present models, the obtained results are compared with the available results of the open literature as well as the results of two software are compared using Root Mean Square Error (RMSE) and good agreements are found. Numerical analyses are performed considering different values of the external load, rigid circular radius, quarter planes span length and material properties. The contact lengths and contact stresses of these values are examined, and their results are presented. Consequently, it is concluded that the considered non-dimensional quantities have noteworthy influence on the contact lengths and contact stress distributions, additionally if FEM analysis is used correctly, it can be an efficient alternative method to the analytical solutions that need time.