The paper proposes a new computational approach using the moving element method (MEM) for simulating the dynamic responses of Mindlin plate resting on a viscoelastic foundation subjected to moving loads during abrupt braking. In this approach, the governing equations as well as the plate element mass, damping and stiffness matrices are formulated in a convected coordinate in which the origin is attached to the applied point of the moving load. Thus, the proposed method simply treats the moving loads as ‘stationary’ at the nodes of the plate to avoid updating the locations of moving loads due to the change of the contact points on the plate. The interaction between the moving load and the plate during abrupt braking is accounted for through the vertical force and tangential wheel-pavement friction force. The effects of wheel sliding, load deceleration magnitude, friction coefficient, and plate thickness on the dynamic responses of plate are investigated.