In this paper, an attempt is made to analyze the impulsive stress directly underneath the concentrated impact point for a supported square plate by using the three-dimensional dynamic theory of elasticity and the potential theory of displacement (stress function) on the supposition that the load, F$_{*}$0 sin .omega.t, acted on the central part of it. The results obtained from this study are as follows: 1. The impulsive stress cannot be analyzed directly underneath the acting point of concenrated impact load in privious theories, but can be analyzed by using the three-dimensional dynamic theory of elasticity and the potential theory of displacement. 2. Theorically, with increasing the pulse width of applied load, it was possible to clarify that the amount of stress in the point of concentrated impact load was increased and that of stress per unit impulse was decreased. 3. The numerical inversion of laplace transformation by the use of the F.F.T algorithm contributes the reduction of C.P.U time and the improvement of the accuracy or results. 4. In this paper recommended, it is found that the approximate equation of impact load function P (.tau.) = A.tau. exp (-B.tau.), and P (.tau.) =0.85A exp (-B.tau.) sinC.tau. could actually apply to all impact problem. In compared with the experimental results, the propriety of the analytical method is reasonable.