The modified theory of elastic stress waves asserts that the wave equations governing volume strain are consistent with existing theories, but a new set of weakly coupled wave equations encompassing both volume strain and partial strain has been developed. To address the problem of stress wave fluctuation caused by a concentrated load impact on a rectangular plate, two sets of control equations for stress wave propagation as well as the fluctuation boundary conditions of loading surface and free surface are established in this paper. The finite difference method is used to solve the wave equation, and the stress wave is simulated numerically for the propagation of the main and secondary waves and the reflection process of oblique incident waves on the free plane. During propagation, the partial strain splits into two parts: one part propagates together with the volume strain, forming the main wave, while the other part propagates at a slower pace, resulting in the formation of a secondary wave. The numerical simulation results show complete consistency with regard to the propagation image of the stress waves in the nanocalcium glass plate under shock loading.