Investigations of kinematic and dynamic models of tractor-trailer systems have historically been performed for stability analysis or state estimation. In this work, we present and evaluate kinematic and dynamic tractor-trailer models for model predictive control (MPC). We show in open-loop simulations that a kinematic and a dynamic model are equivalent at low speeds and short discretization time steps. A zero speed singularity and stiff dynamics prevents the usage of the dynamic model in control design, where discretization time steps are longer. A method of discretization is proposed to resolve the low speed feasibility of the dynamic model. In closed-loop simulations, the real-time applicability of the kinematic and dynamic models in a nonlinear MPC is verified.