An endochronic viscoplastic approach, derived from the theory of finite viscoplasticity based on material isomorphisms, is presented, in order to describe the nonlinear material behaviour of filled polytetrafluoroethylene (PTFE) in a computational analysis of PTFE shaft seals. The model allows to characterize viscoplastic material behaviour with an equilibrium hysteresis using a rate-independent elastoplastic model (with an endochronic flow rule and a logarithmic elastic law) in parallel connection with a nonlinear Maxwell model. Due to the endochronic flow rule, an elastic range limited by a yield stress is not needed in the present approach. The volumetric stress contribution is assumed to be purely elastic. The proposed model is applied to simulate the mounting process of PTFE shaft seals in an axially symmetric finite element analysis. The numerical results (radial force, pressure in the contact zone) are in fair agreement with the experimental data.