Based on a higher older plate theory, non-linear partial differential equations for the vibrating motion of a plate are derived. By using these equations, the large amplitude vibration of a simply supported rectangular plate is investigated. By neglecting the higher order terms and introducing the shear correction factor into the governing equations, the present higher order plate theory can be reduced to the first order Mindlin plate theory. The Galerkin method is used to transform the governing non-linear partial differential equations to ordinary non-linear differential equations. The Runge-Kutta method is used to obtain the linear and non-linear frequencies. The linear (natural) frequency can be obtained by neglecting non-linear terms: i.e., the von Karman assumption is not considered. From comparing the present 11 variables higher order plate theory results with the five variables Mindlin plate theory results, it can be concluded that the higher order shear deformation terms have a significant influence on large vibration of plates. (C) 1995 Academic Press Limited.