This paper treats the bending problem of a uniformly or concentratedly loaded circular plate subjected to elastic constraint for the deflection at its edge, i. e., elastic support. It is assumed that the degree of the constraint varies periodically and stepwisely or continuously along the edge of the circular plate. The iterative method which was previously proposed by the authors for the problem of the circular plate with mixed boundary conditions is adopted in this paper. The case when the degree of constraint varies nonlinearly according to the deflection at the edge is also considered.