In order to study the dynamic response of the asphalt pavement under vehicle random stimulation, the random vibration model of vehicles and the mathematic model of pavement dynamic response in which the base and surface are all viscoelasticity are established respectively. The analytical solution of the stochastic response for the pavement is deduced. The stochastic load acted on the pavement can be gotten by the mathematic model of the vehicle vibration. The numeral feature functions of the random response, such as even function, time-space correlation function, time correlation function and mean square function, are obtained by the analytical solution. The paper provides a theory method for studying the random response of the asphalt pavement.