Geometrically nonlinear bending analysis of clamped circular plates under axisymmetrical transverse load is made in this computational study. The thickness of the plate is considered to be uniform and the plate material is assumed to be isotropic and homogeneous. Since both the plate geometry and the loading are axisymmetric a set of nonlinear ordinary differential equations are solved in the paper. The system of nonlinear algebraic equations which is obtained by the finite difference method is solved by the Newton-Raphson method. The boundary conditions at the support and at the center of the plate are satisfied exactly. The accuracy of the results is verified by checking the maximum deflection with the results available in the literature. In case of uniform pressure almost identical central deflection is obtained.