The response of an infinite elastic plate to dynamic loading is presented by the method of superposition of normal modes, a method particularly appropriate in the intermediate and far field. The method is compared with the method of integral transforms. Explicit expressions are given for the case of loading by a concentrated vertical step force. These expressions are evaluated numerically over a range of distances from 4 to 40 plate thicknesses. The numerical results are compared with qualitative stationary phase analyses and with the exact results of generalized ray theory.