This work is motivated by the fact that the surface of a road may vary with local pavement properties and number of passes of the vehicle, which means the roughness coefficient and waviness of the road may vary in specific intervals. However in traditional random road models, the roughness coefficient and waviness of the road are assumed as constants. Therefore this assumption may be not very reasonable. A novel random road model is presented where the roughness coefficient and waviness of the road are expressed by interval numbers instead of constants. A framework for computation and analysis of vehicle ride dynamics under random terrain excitation with interval parameters is established in the frequency domain. For simplicity, a 5-degree-of-freedom ride dynamic model of the vehicle is derived as a numerical example. The power spectral density (PSD) and root mean square value (RMS) of the vehicle ride responses are shown and analyzed. Analysis results indicate that the vehicle responses vary in specific intervals under the random road excitation with interval parameters.