The random vibration analysis of a four-wheeled vehicle traveling on parallel road tracks with random unevenness is considered. The two parallel road track roughnesses are modeled as a vector of homogeneous, non-isotropic, Gaussian random fields with known auto-power spectral density (PSD) functions but unknown cross–PSD functions. Questions on bounds on the response, when the unknown cross-PSD functions are varied over their permitted ranges, are considered. An exact solution to this problem, based on principles of random vibrations, is arrived at. Based on this theoretical solution, an experimental procedure to determine these response bounds on automotive structural response, without involving mathematical idealization of structural matrices, is developed. Illustrations involving numerical modeling and laboratory testing (using a four-post test rig) of vibratory behavior of a four-wheeled vehicle due to random road loads are presented.