For the first time, the single-axle-two-wheel test vehicle is used to detect the damage of a plate-type bridge that is simply supported at the two longitudinal ends, but free on the lateral sides. The test vehicle with two wheels is refined as a two degree-of-freedom (DOF) system to capture the motions in both the longitudinal and lateral directions. The vehicle response recorded or calculated has been criticized for the vehicle frequencies’ overshadowing effect on the bridge frequencies to be identified in spectral analysis. To overcome this problem, the vehicle-bridge contact response (that is free of vehicle’s frequencies) is used instead to single out the bridge frequencies, while extracting the mode shapes. Central to this study is the newly presented uniform translational response (UTR) for damage localization of the plate, which is physically more meaningful than its predecessor. The UTR vector can be computed for each wheel by considering the first few flexural modes scanned from the contact response along its moving path. Based on the correlation between the two UTR curvatures generated for the left and right wheels of the test vehicle, the location of each damage can be identified. Illustrative examples show that the proposed method works well in estimating the longitudinal locations and lateral extents of the damages in the plate structure. Parametric study has further verified the effectiveness and robustness of the proposed method under various conditions.