The design of motion controllers that could reduce terrain disturbances propagated to the arm and optimize the trajectories of skid-steer mobile manipulators (SSMMs) working in agricultural, construction, or mining environments requires accurate physical models capable of correctly representing disturbances caused by changes in terrain slope, loss of traction, and other wheel-ground interactions. Therefore, this paper develops the forward dynamics equations of motion and proposes a general model for SSMMs. The novelty of the model is that it considers a floating-base with nonpermanent wheel-ground contacts, i.e., the mobile base has 6-degree of freedom (DOF) and the wheels may lose contact with the terrain. Unlike the existing models, the proposed one is general because the procedure can be extended to MMs with an arbitrary number of arms or wheels and does not restrict the mobile base to planar 2-D motions. Furthermore, it takes into account the loss of traction and the deformation of the wheel-ground contacts. The experimental results involving a small SSMM with a 3-DOF arm and an industrial skid-steer loader validate the physical fidelity of the model. Although the focus of this paper is not in control aspects, one of the examples shows the role physically accurate models can have in the design of end-effector motion controllers, and its potential application to the design of controllers capable of decoupling the arm motion from ground disturbances.