The research introduces a numerical method for solving the problem of an axisymmetric rigid smooth body indenting an incompressible elastic layer. This study proposes a computational approach with the deformed mesh interface in the COMSOL Multiphysics software, which allows the discretized interior nodes to move by solving PDEs for the mesh displacements with the given slope boundary condition. The proposed method is applied to the indentation problems with spherical and conical smooth axisymmetric indenters. The results are in a good agreement with the analytical solutions, and the method shows rapid convergence.