In this paper, the rigid roadway pavement under dynamic traffic loads with variable velocity is studied. The rigid roadway pavement is modeled as a rectangular damped orthotropic plate supported by elastic Pasternak foundation. The boundaries of the plate are the steel dowels and tie bars which provide the elastic vertical support and the rotational restraint. The natural frequencies and the modal shapes of the system are obtained through solving two transcendental equations, derived from the solution of two auxiliary Levy's type problems, known as the Modified Bolotin Method. The dynamic moving traffic load is expressed as a concentrated load of harmonically varying magnitude, moving straight along the plate with a variable velocity. The dynamic response of the plate is obtained by using the characteristic equation with orthogonal properties. The results of a numerical example show that the velocity and the angular frequency of the loads affect the maximum dynamic deflection of the rigid roadway pavement. It is also shown that a critical speed of the load exists. If the moving traffic load travels at the critical speed, the rectangular plate will suffer from a deflection of infinite amplitude. The present mathematical solution should be verified further with the results of experimental researches, especially, with respect to the determination of the forces in the steel connecting devices (dowels and tie bars) along the joints.