This paper describes a finite strain elasto-viscoplastic constitutive model to predict the non-linear behaviour of polymeric based materials. The theoretical basis of the material model and the computational treatment are presented. The operator split methodology and the Newton–Raphson method are used to derive the state update algorithm and to obtain the numerical solution. The integration algorithm reduces to the solution of only one scalar non-linear equation. A closed formula for the corresponding consistent tangent operator is presented. Different aspects of the constitutive model and its integration algorithm are investigated by considering a comprehensive set of numerical examples.