It is shown that the true reason of existing inconsistency at comparison of the Hertz–Belyaev classical solutions of contact problems with the numerical solutions, obtained by finite element method ( FEM) for canonical-formed elastic bodies contact more often is not the unsubstantially declared poor precision of the numerical method, but the substantial distortion of the contact elements curvature, which causes accuracy of classical solutions. The criteria of reliable accuracy evaluation of classical and numerical solutions of contact problems at measuring the maximal shear stresses and the depth of its occurrence are given.