The paper proposes a computational approach to simulate the dynamic responses of composite plate resting on a Pasternak foundation subjected a moving load using the moving element method (MEM). The plate element stiffness matrix is formulated in a coordinate system which moves with the load. The main convenience is that the load is static in this coordinate system, which avoids the updating of the load locations due to the change of the contact points with the elements. The effects of the Pasternak foundation, energy dissipation mechanisms, load’s velocity, material properties on the dynamic responses of the composite plates are investigated.