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The purpose of this research is to study the vibration and acoustic pressure radiation from a thin isotropic flat plate stiffened by a rectangular array of beams, and excited by a time harmonic point force. These constructions on aircraft and ship structures are often subjected to frequency dependent pressure fluctuations and forces. Forces from the these excitations induce structural vibrations in a wide range of frequencies, which may cause such things as acoustic fatigue and internal cabin noise in the aircraft. It is thus important that the response characteristics and vibration modes of such periodic structures be known. From this theoretical model, the sound pressure levels(SPL) in a semi-infinite fluid(water) bounded by the plate with the variation in the locations of an external time harmonic point force on the plate can be calculated efficiently using three numerical tools such as the Gauss-Jordan method, the LU decomposition method and the IMSL numerical package.