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Composite materials also known as fiber reinforced plastics have been developed and used in many engineering applications due to their outstanding mechanical properties. Laminated plates as structural components that are made of in composite material are widely used. Composite laminae have strongly anisotropic properties and display significantly nonlinear behavior when loaded in shear. While such components have been used for over a decade, their design has predominantly been performed using deterministic methods. In this study, the method of equivalent linearization is used in conjunction with the finite element method to perform nonlinear random vibration analysis of laminated composite plates. The classical laminated plate theory is used to account for the variation of strains through the thickness for modeling laminated composite plates. The displacement, strain and stress response are computed at different excitation load levels. The results indicates that the effect of nonlinearity on the responses for any given load level depends on the ply arrangement and becomes more significant for higher excitations.