The stretch blow moulding process for polyethylene terephthalate (PET) bottles generates important modifications of the mechanical properties of the material as it can be shown in an identification study of the orthotropic and heterogeneous elastic properties in the 3D region of the petaloïd bottom of PET bottles. The main topic of this work deals with the modelling of the complex behaviour of the PET during the process that is managed at a temperature slightly above the glass transition temperature Tg. In this range of temperature and considering the high strain rates involved during the process, large changes in the material morphology can be observed and the goal of this work is to propose a visco hyperelastic model to predict the PET behaviour under these severe conditions: large deformations, high strain rate… An original procedure is proposed to manage the identification of the material properties from the experimental data of recent biaxial elongation tests. On the other hand, effects of temperature are of fundamental importance during the injection stretch blow moulding process of PET bottles. Near Tg small variations of temperature have great influence on physical properties: an accurate prediction of the initial temperature field generated by the infrared heating is proposed. Also, the important viscous dissipation induces self-heating of the material during the process which is necessary to be taken into account during the numerical simulation. The identification of the thermal parameters is achieved by an experimental infrared heating study. The global thermo mechanical model is implemented and numerical simulations are managed using the finite element method to solve the free blowing of PET preforms