It is necessary to model and simulate the time histories of the road for ride dynamics of a vehicle subjected to the stochastic road excitation. This paper focuses on the mathematical model, algorithm design and simulation realization of road in time domain. The methods converting the frequency domain model of road irregularity to the time domain model were analyzed and the correlations between vehicle wheels and between tracks were taken into account in modeling the numerical road. Three main algorithms, harmony superposition, white noise filtration, and Inverse Fast Fourier Transform (IFFT) ...