In this work, the non-linear dynamic instability and responses parametric vibration of sandwich composite plates subjected to periodic in-plane compressive load applied along two opposite edges are theoretically analyzed using the extended dynamic stiffness method. The problem is solved for four different sets of boundary conditions. The authors present how to establish the exact dynamic stiffness matrices of rectangular sandwich plates subjected to periodic in-plane forces based on von Karman’s large deflection plate theory. A set of second-order ordinary differential nonlinear equations of extended Mathieu-Hill type with periodic coefficients is formed to determine the regions of parametric instability and non-linear responses based on Bolotin’s method. Therefore, the... nonlinear temporal response of the system is obtained next. The effects of various parameters such as static load factor, dynamic load factor, aspect ratio, excitation frequency, and boundary conditions on the regions of dynamic instability and the nonlinear parametric vibration characteristics of the plate for principal parametric resonances are studied in detail.