This investigation assesses the capability of an approximate method to predict the response of a missile penetration presents how to apply the Rayleigh-Ritz method to the missile penetration problem. The main purpose of this work is generating the approximate method more accurately than the simplified analysis method, still retaining the simplicity. The results of the 3-modes assumption are compared with those of the detailed analysis and the test data available. It is shown that they are in cloy agreement to predict the missle penetration.