The interaction between deformable terrain and wheels significantly affects wheel mobility. To accurately predict vehicle mobility or optimize wheel design, an analysis of this interaction is essential. This study develops a hybrid terramechanics model (HTM) that integrates the semi-empirical model (SEM) and the discrete element method (DEM) using artificial neural networks (ANNs). The model overcomes the limitations inherent in SEM and DEM approaches. We used DEM simulations to analyze the impact of wheel design parameters and slip ratio on terrain behavior. ANNs were subsequently developed to predict dynamic sinkage in real time based on these results. A new concept, termed bulldozing angle, was introduced to define additional terrain–wheel contact caused by dynamic sinkage. Based on this concept, we predicted the bulldozing resistance exerted on the wheel. By combining SEM, ANNs, and DEM, we developed an HTM capable of terrain behavior analysis. Lastly, we conducted a comparative analysis between the SEM, HTM, and actual test data. The results confirmed that the predictive accuracy of the HTM surpassed that of the SEM across all slip ratios.