The effects of local-damaged cover on a mechanical elastic tire are studied in terms of static and dynamic characteristics. First, the nonlinear finite element model of the tire is established according to its working principle and structure. The natural frequency and vibration mode of a normal tire are calculated using modal analysis of its finite element. Then, the main faults and dangerous areas of the tire are analyzed considering its mechanical features and past use. A tire with varying local damage at different positions is simulated using the stiffness degradation model for its changing natural frequency and mechanics characteristics under static-ground-bearing condition. Finally, the dynamic stress response of the local-damaged tire to the random roughness of a B-level road is studied. Research shows that natural frequency is reduced with more severe damage, but the location of the maximum stress remains the same while the peak stress value gradually increases; the local-damaged tire′s peak value of dynamic stress response is greater than that of a normal one, and its resonance frequencies change; and the peak value of dynamic stress response to more severe damage at the resonance frequency increases, but changes little during other frequency bands.