The submitted paper is dedicated to the numerical simulation of moving load effect on road structures in the time domain. The dynamic load from vehicles on pavements is the subject of interest. The multi- body computing models of vehicles on various levels are introduces. The equations of motions are derived in the form of ordinary differential equations. The equations of motions are solved numerically by the use of step-by-step integration method in the environment of program system MATLAB. The road unevenness as the main source of kinematical excitation of vehicle is modeled as the random rod profile by the use of the power spectral density functions. The time histories of wonted functions are calculated. Especially the time histories of tire forces as the source of dynamic load of pavements are the object of interest. The conclusions are focused on the influence of the road profile quality on the values of tire forces.