The assumptions of statistical theory of rough surfaces contact based on a "compliance depth" have been critically analyzed. The equations for contact parameters resulting from the theory are of complex multiple parametric integral forms and for their solutions computer techniques have been applied. It follows from the comparison of the contact parameter values obtained for the systems with one and two rough surfaces that the models differ considerably and it is not possible to replace more complex system including two rough surfaces by means of a simpler model with only one such a surface.