This paper presents a method to identify material parameters of a hyperelasto-visco-hysteresis (HVH) model and its application for the simulation of a fluoro-elastomer behaviour. This 3D-phenomenological model is based on the additive decomposition of three stress components. Each of these constitutive stresses is related to a physical phenomenon that occurs during mechanical loading: a hyperelastic equilibrium stress response, an irreversible pure hysteresis stress contribution and a rate-dependent viscoelastic stress behaviour. In order to independently identify these parts of the model, an experimental campaign, including multi-step relaxation in traction and compression tests and simple relaxation in tension and compression tests, is used. The hysteretic and hyperelastic contributions are identified considering only the state at the end of the relaxation periods of the multi-step relaxation tests. The viscoelastic response is analytically calculated with the simple relaxation test. As an advantage, the developed identification scheme gives the possibility to discriminate all the stress components of the model. Finally, the numerical simulation of a seal in relaxation is carried out to verify the capability of the proposed HVH model by reproducing the mechanical response of the studied material.