The theoretical analysis depends on the Classical Laminated Plate Theory (CLPT) that is based on the Von-K ráman Theory and Kirchhov Hypothesis in the deflection analysis during elastic limit as well as the Hooke's laws of calculation the stresses. New function for boundary condition is used to solve the forth degree of differential equations which depends on variety sources of advanced engineering mathematics. The behavior of composite laminated plates, symmetric and anti-symmetric of cross-ply angle, under out-of-plane loads (uniform distributed loads) with two different boundary conditions are investigated to obtain the central deflection for mid-plane by using the Ritz method. The computer programs is built using Mat lab(R2011a), to solve non-linearity effects on the central deflection values of rectangular cross-ply composite laminated plates, aspect ratio, stresses, orthotropic factor (E/G) and orientations of fiber. The non-linear analysis results of (4.74%) for SSSS of / / cross-ply angle plate, (8.77%) for CCCC of / cross-ply angle plate and (10.83%) for CCCC of / / cross-ply angle plate showed a good agreement with Reddy, 1997 results.

          Comparing between the analytical linear, non-linear and experimental results gave a big difference  between linear and non-linear results, while, non-linear showed close results with  experimental results.