This paper is concerned with a method for solving dynamic response problems of arbitrarily shaped plates in contact with a fluid. By utilizing the Fourier expansion and the Laplace transform methods for disposing of general dynamic pressures, and by applying the Fourier expansion collocation method for satisfying the boundary conditions, expressions for the dynamic response of displacement and bending moment are obtained in a general form which is applicable to general dynamic pressures and arbitrarily shaped plates. Numerical calculations have been carried out for circular plates, rectangular plates, rectangular plates with round corners, and oval plates. The results obtained in certain plates are compared with the exact ones.