An analysis based on linear theory is presented for determining the dynamic response and the conditions of resonance for a simply supported rectangular plate acted upon by two types of moving loads corresponding to: (1) a point force of variable magnitude oscillating about a fixed position on the plate, and (2) a point force of constant magnitude traveling in a circular orbit about a fixed position on the plate. In addition to the ordinary resonance as produced by a variable magnitude load concentrated at a fixed position on the plate, resonance of the plate may occur due to the changing position of the load on the plate. It is shown that an infinitely countable number of load movement frequencies may excite a given principal frequency of the plate for them,nth mode of vibration. Numerical examples of typical deflection profiles and time rate of deflection buildup are presented for two sets of initial conditions corresponding to: (1) a load initially at rest on the deflected beam, and (2) an accelerating load dropped from zero height on an initally undeformed beam.