In the development of lunar and planetary exploration rovers, risk assessment in on-site environments comprising fine regoliths and unevenly distributed rocks is essential. To prevent a rover from being stuck during its operation, one must understand the behavior of its wheel when it climbs over rigid obstacles in off-road environments. In this study, we apply an extended terramechanics model, which can reasonably describe the interaction between soft ground and vehicles, to analyze the obstacle-climbing behavior of rigid wheels. To describe the interaction between the wheel and a hard obstacle, we combine the penalty method with the extended terramechanics model. Subsequently, we verify the effectiveness of the proposed method by comparing its results with those of a traversing single wheel obtained from a laboratory experiment. Furthermore, we use the model to perform a multibody dynamics analysis on a simple rover, where its applicability to the examination of the overall performance of obstacle climbing is demonstrated.