This work is motivated by the fact that the surface of a terrain may vary with local pavement properties and number of passes of the vehicle, which means the roughness coefficient and waviness of the terrain may vary in specific intervals. However, in traditional random terrain models, the roughness coefficient and waviness of the terrain are assumed as constants. Therefore, this assumption may be not very reasonable. A novel random terrain model is presented where the roughness coefficient and waviness of the terrain are expressed by interval numbers instead of constants. A 5-degree-of-freedom ride dynamic model of the vehicle with uncertain parameters is derived. 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 terrain excitation with interval parameters.