Abstract: 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) based on road power spectral density (PSD), were designed and integrated as a system of road simulation constructed on the MATLAB software platform. For the simulation to be as realistic as possible, several important aspects, including the bi-lateral track relation in time domain, the improvement of simulation algorithm and the integration of the methods were emphasized. The simulation example demonstrates that the applied methods are general and efficient, and the resulting time domain road agrees fairly well with the reality.