To analyze the yaw and rollover stability of an off-road vehicle with mechanical elastic wheel (MEW), based on the brush tire model, a corrected steady-state combined longitudinal-slip and cornering brush models of MEW is set up. The flat-bed test rig of tire mechanical properties is used to conduct the steady-state longitudinal-slip and cornering characteristics experiment of the MEW and pneumatic tire, respectively, and the mechanical properties of MEW are analyzed based on the experiment results. Then, a nonlinear off-road vehicle simulation model with MEW is established to evaluate the yaw and rollover stability based on Carsim, which utilizes yaw rate and predictive load transfer ratio (PLTR) as the yaw and rollover index respectively. The cornering properties of MEW to yaw and rollover stability are analyzed based on phase-plane. Compared analysis of the cornering characteristics of pneumatic tire and MEW are done and the results show that the changed trend of cornering characteristic curve and the peak value of lateral force are almost the same, but the cornering stiffness of MEW is bigger and the vehicle with MEW has a good stability of rollover but yaw, furthermore, as peak value of lateral force increases and lateral stiffness decreases properly, the vehicle can achieve a better stability of yaw and rollover. The above simulations will be useful for the improvement and optimization of cornering performance and structure parameters of MEW.