This paper establishes the internal mathematical and energetic consistency of a hybrid-dynamical-system, lumped-parameter, planar, physical model for capturing transient interactions between an elastically deformable tire and an elastically deformable terrain as a baseline result for more realistic models that account for permanent deformation, shear failure, and three-dimensional contact conditions. The model accounts for radial and circumferential deformation of the tire as well as normal and tangential deformation of the terrain. It captures the onset and loss of contact as well as localized stick and slip phases for each of the discrete tire elements by a suitable evolution of a collection of associated internal state variables. The analysis characterizes generic transitions between distinct phases of contact uniquely in forward time and proves that all internal state variables remain bounded during compact intervals of contact. The behavior of the model is further illustrated through an analytical and numerical study of two instances of tire-terrain interactions under steady state condition.