The mechanical behavior of polyethylene terephthalate (PET) under the severe loading conditions of the injection stretch blow molding process is strongly dependent on strain rate, strain, and temperature. In this process, the PET near the glass-transition temperature (T-g) highlights a strongly nonlinear elastic and viscous behavior. In the author's previous works, a nonlinear visco-hyperelastic model has been build and identified from equi-biaxial tensile experimental results. Despite the good agreement with biaxial test results, the model fails to reproduce the sequential biaxial test (with constant width during first step) and the shape evolution during the free blowing of preforms. In this work, an anisotropic version of this visco-hyperelastic model is proposed and identified form both equi and constant width results. The new version of the nonlinear visco-hyperelastic model is implemented into the Abaqus environment and used to simulate the free-blowing process. The comparison with the experimental results managed in Queen's University of Belfast validates the approach in terms of bubble shape and thickness distribution. POLYM. ENG. SCI., 2020. (c) 2020 Society of Plastics Engineers