Abstract: Von-Karman type orthotropic rectangular plates with three edges clamped and one edge simply supported are analyzed by Galerkin method. The beam mode vibration functions are employed as displacement functions that accurately satisfy the boundary conditions. The displacement functions have orthogonal property. Governing nonlinear partial differential equations are transferred to an infinite set of systems of nonlinear algebraic equations containing Fourier coefficients. Large scale sparse-matrix linear equations are solved by stabilized biconjugate gradient method and nonlinear algebraic equations are solved by parameter-regulated iterative procedures. The series of beam vibration functions exhibit rapid convergence. Only a few prior terms of the series are truncated to meet the need of computing accuracy. Numerical results of deflection and stresses are obtained for different composite materials.