Tracked vehicles possess excellent terrain adaptability and are widely used in various complex terrains. Simulation of tracked vehicles based on dynamic modeling is an effective means to study the dynamic performance of tracked vehicles and optimize design parameters. The complex contact between the tracked vehicle and the ground often reduces the efficiency and stability of solving the tracked vehicle model. This paper proposes a modeling method that embeds the ground as a geometric constraint into the dynamic model. Given the ground and wheel radius, a nominal wheel center trajectory that does not depend on the vehicle’s driving speed and other vehicle parameters can be pre-calculated. The contact between the wheel and the ground can be transformed into a constraint that the wheel center falls on the nominal trajectory. Based on the magnitude of the ground support force on the load wheels and the position of the wheel center, it can be determined when the wheel contacts the ground. This allows the model to effectively simulate the passing ability of tracked vehicles under challenging ground conditions. The proposed model is validated through simulations on sinusoidal terrains of different frequencies and the terrain with a pothole.