The foundation of the nonlinear theory of asymmetric anisotropic sandwich plates with a first order compressible weak orthotropic core under a Friedlander-Type explosive blast is presented. The equations of motion are developed by means of Hamilton's Principle. Within the theory, the face sheets are asymmetric while adopting the Love-Kirchoff model. In addition, the core layer is assumed to be compressible (extensible) in the transverse direction thereby capturing any wrinkling or global instabilities. The theory is then simplified and applied for the case of sandwich plates with symmetric unidirectional fiber reinforced laminated composite facings with the axes of orthotropy not necessarily coincident with the geometrical axes. The governing solution is developed using the Extended-Galerkin method resulting in two coupled nonlinear second order ordinary differential equations which are then solved using the adaptive 4th-Order Runge-Kutta Method for a system of differential equations.