Energy dissipation is calculated from the contact deformation of a rolling toroidal membrane tire model. The method of dissipation analysis developed here can be used with other structural representations, including those based on the finite element method. The membrane tire model is inflated, loaded, and rolling on a frictionless, flat surface. The membrane material is assumed to be isotropic and neohookean under static loads and to exhibit a low loss tangent. The assumption of a low loss material permits viscoelastic power loss to be calculated from load transfer functions derived from the elastic response of the tire model. The power loss calculation is used to predict rolling resistance and contact patch shift.