Abstract: In the paper, von-Karman type orthotropic rectangular plates with two adjacent edges simply supported and the other two adjacent edges clamped are analysed by using Galerkin method.The beam vibration functions are taken as displacement functions that may accurately satisfy the boundary conditions, and have orthogonality property.The governing nonlinear partial differential equations are reduced to an infinite set of systems of nonlinear algebraic equations containing Fourier coefficients which have been solved by linearizing iterative procedures. The series of beam vibration functions are rapidly converged. Only a few items of the series may meet the need of accuracy. Numerical results of deflection and stress are obtained for different composite materials.