The vibrational characteristics of a plate on a two-parameter foundation under moving rectangular loads with variable velocities are investigated, and the general solution for the dynamic deflection of the plate is derived using the double Fourier transform. Employing the fast Fourier Transform, a rigid pavement is chosen to obtain numerical results, which are consistent with those from the classical solution. The effects of initial load velocity, load acceleration, load deceleration and horizontal resistance at the plate bottom on the dynamic deflection are discussed. An expression to predict the critical velocity is derived, and the results from this formula show very good agreement with those from the numerical analysis. The numerical analysis indicates that the maximum dynamic deflection occurs when the load velocity reaches the critical velocity for the plate. The initial velocity, the acceleration and the deceleration of the rectangular load influence the dynamic response, and the dynamic deflection of the plate at the critical velocity decreases significantly as they increases
