Recently, autonomous field robots have been investigated as a labor-reducing means to scout through commercial strawberry fields for disease detection or fruit harvesting. To achieve accurate over-bed and cross-bed motions, it is preferred to design the motion controller based on a precise dynamic model. Here, a dynamic model is developed for a custom-designed strawberry field robot considering terramechanic wheel–terrain interaction. Different from existing models, a torus geometry is considered for the wheels. In order to obtain a control affine model, the longitudinal force is curve-fitted using a polynomial function of the slip/skid ratio, while the lateral force is curve-fitted using an exponential function of both the slip/skid ratio and slip angle. An extended Kalman filter (EKF) is then developed to estimate the unknown parameters in the approximated model such that the state variables propagated by such a model can match experimental data. The approximated model and the EKF-based parameter estimation method are then validated in a commercial strawberry farm.