Tire wear cost accounts for a large proportion of the total cost of heavy mining dump trucks (HMDTs), and the shimmy of the steering system aggravates the tire wear severely. This study proposes a model-based approach to avoid the shimmy of the steering system for such trucks without replacement or destruction of steering structure. First, a five degrees-of-freedom (DOF) shimmy dynamic model of the steering system is established considering the tire lateral dynamics and the nonlinearity of the hydro-pneumatic suspension (HPS). Second, the unstable parameter range of the dynamic model is obtained based on the Lyapunov’s first approximation theorem and Hopf bifurcation theory. The stability analysis results show that the steering system of heavy mining dump trucks is a self-excited vibration system because of the Hopf bifurcation in the unstable parameter range, and this unstable parameter range is greatly affected by the load and the initial pneumatic volume of hydro-pneumatic suspension. In addition, the accuracy of the dynamic is verified by a field test. Therefore, how the load and initial pneumatic volume affect the shimming is analyzed numerically. In other words, how to match the load and initial pneumatic volume is uncovered to avoid the shimmy. For instance, it shows that the shimmy at full load can be avoided at the speed of 30 km/h by charging the initial pneumatic volume of hydro-pneumatic suspension to 14.5 l.