Numerical simulation of the heating stage of thermoplastics in thermoforming requires a good knowledge of the behavior of the materials used. To this end, a study is being conducted on the characterization of the viscoelastic behavior of a circular membrane, made of high-density polyethylene (HDPE), under the combined effect of temperature and the force of gravity. The experimental tests were carried out in a convection oven for five temperatures (100, 110, 120, 130 and 140 C). For the numerical characterization of the viscoelastic behavior, two viscoelastic models were considered: the classic Kelvin-Voigt model and the new three-parameter modified Burger's model (Jeffrey model) that we propose. The mechanical parameters of both models were identified using the Levenberg-Marquardt algorithm. The thermal-dependency of the viscosity was characterized by two thermal models: the Arrhenius law and the William-Landel-Ferry (WLF) equation.