A finite element method was applied to analyze the dynamic response of slab track subjected to a moving load. The slab track was treated as a model, in which rail was regarded as a long beam supported by discrete viscoelastic supports, and slab as a short beam supported by continuously viscoelastic foundation. The slab track and moving load were considered as a system. Vibration equations of the system could be formulated by using the principle of total potential energy with stationary value in elastic system dynamics and the "set-in-right-position"rule for formulating matrixes. The effects of the speed of the moving load, the rail type, and the spring stiffness of rail support on the response of rail and slab were studied. From the presented numerical examples, when the other parameters being the same, with the increasing of spring stiffness of rail support, the dynamic response of rail decreases; with the increasing of rail type, the dynamic response of rail and slab decreases; with the increasing of moving load speed, the dynamic response of rail and slab increases.