This paper describes vibration analysis using fast finite element method for an automotive sound proof structure with body frames supported by nonlinear concentrated springs. The sound proof structure is constituted of a porous material sandwiched between a steel panel and a cover plate. And we use three-dimensional finite elements and Modal Strain and Kinetic Method to express the damped dynamic motions of the structure. Restoring forces of the nonlinear springs have cubic nonlinearity. The discretized equations for the global system in physical coordinate are transformed into the nonlinear ordinary coupled equations using normal coordinate corresponding to linear natural modes. This transformation yields computation efficiency. The structure is excited periodically. We computed nonlinear stationary and non-stationary responses due to internal resonance in coupling modes between the nonlinear springs and the sound proof structure under large input. The non-stationary motions are confirmed as the chaos due to maximum Lyapunov exponents with a positive number. From the time histories of deformation distribution in the chaotic vibration, we found out nonlinear modal couplings.