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The free and forced nonlinear vibration of the fixed and simply supported, orthotropic annular plates with stepwise are investigated. Assuming
harmonic oscilations, and utilization of Ritz-Kantorovich method the time variable
is eliminated. Hence, the governing nonlinear partial differential equations for the axisymmetric vibration of annular plate are reduced to a set of ordinary nonlinear differential equations. The finite difference
method together with multidimensional Newton Raphson method is used for
solution of problem. The initial guesses for starting the solution are obtained from the I inear solution of plate. Modes shapes, frequency, bending and membrane stresses for two case of fixed and simply supported are compared. For particular problem,
finite difference gives the same results as those of shooting method with less
intervals (points) chosen for numerical solutions.