A multimode time-domain modal formulation based on the finite element method for large-amplitude free vibration of thin composite plates is presented. Accurate frequency-maximum deflection relations can be predicted for the fundamental and the higher nonlinear modes. A modal participation is defined, and accurate and convergent frequencies can be determined with minimum number of linear modes. A procedure for the selection of initial conditions for periodic plate response is presented. Convergence of frequency with gridwork refinement and number of linear modes is studied. The classical single-mode elliptic function frequency solutions for simply supported beams and square plates are assessed. Examples of orthotropic and composite plates are given, and the characteristics of nonlinear response are studied.