The present work is dedicated to a sector market of Trelleborg Boots: the constant velocity joint boots (CVJ). During their use, joints are subjected to severe constraints such as wide temperature range, self-contact, friction between coils or grease. In order to increase their lifespan, Trelleborg Boots is investigating new materials and particularly thermoplastics copolyester-ether (TPE-E). The later exhibits some mechanical properties similar to rubber which includes large deformations, viscoelasticity, incompressibility… However, an experimental campaign shows that viscoplastic effects must be considered. Consequently, as both rubber-like and metallic-like models of the literature are not suitable for TPE-E, a new one is proposed in order to predict the CVJ behavior by finite element (FE) analysis. Based on a multiplicative decomposition of the deformation gradient tensor, the constitutive model is inspired by the Bergström and Boyce model (Bergström and Boyce 1998) and written in a thermodynamical formalism. Both hyperelastic and damage parts are inspired by the GDM model (Gornet et al. 2012) and extended with a viscoelastic behavior. Finally, the viscoplastic part is based on the work done by (Shutov and Kreißig 2008).