The governing differential equation of motion of a thin rectangular plate excited by a moving mass is considered. The moving mass is traversing on the plate’s surface at arbitrary trajectories. Eigenfunction expansion method is employed to solve the constitutive equation of motion for various boundary conditions. Approximate and exact expressions of the inertial effects are adopted for the problem formulation. In the approximate formulation, only the vertical acceleration component of the moving mass is considered while in the exact formulation all the convective acceleration components are included in the problem formulation as well. Parametric studies are carried out to investigate the effects of moving mass weight and velocity as well as its trajectory on the dynamic response of a simply supported plate. Rectilinear and orbiting paths are considered in the parametric studies as the two limiting cases for any possible moving mass trajectories. The obtained results demonstrate the importance of the moving mass inertia with respect to the moving load in most of the cases considered. In case of the rectilinear path, the approximate formulation underestimates the plate’s maximum response for mass velocities above certain limits. Furthermore, increasing the plate’s aspect ratio or the moving mass weight further reduces the range of velocities in which the approximate formulation can be used instead of the exact formulation. For the case of an orbiting path, the approximate formulation can capture the resonance excitation frequencies of the load reasonably well, even for large mass weight and radius of the orbiting mass. Considering small orbiting mass radii, the approximate formulation would provide an upper bound for the true response of the system for all orbiting frequencies as well as the mass weights. However, for larger radii, the maximum response values resulting from the approximate formulation are considerably lower than that of the exact one, especially for frequencies near to the resonance frequencies.