Since the traditional tracked vehicle steering mechanical model ignores the influence of centrifugal force, we set up a Caterpillar vehicle steering mathematical model under the influence of the centrifugal force and track slip/slide. The proposed model contributed to the accurate calculation of various performance parameters of the tracked vehicle in the actual steering process on the basis of thorough study on the tracked vehicle steering mechanism. We took a specific tracked vehicle as an example for a numerical solution. The results showed that when considering the influence of centrifugal force, the ground pressure distribution of tracked vehicle presented a trapezoidal shape rather than the uniform distribution demonstrated in traditional theory. The steering performance was also influenced by track slip/slide when the vehicle drove on stickier soil. Finally, the practical test proved the model’s validity. The findings provide a theoretical basis to the design of the crawler, caterpillar vehicles structure optimization and smooth control of the vehicles steering.