In this work, we are interested, on the one hand in the characterization of circular polymeric ABS and HIPS membrane under biaxial deformation using the bubble inflation technique, on the other hand in modelling and numerical simulation of the thermoforming of ABS and HIPS materials using the dynamic finite element method. Hyperelastic models (Mooney-Rivlin, Ogden) are considered. First, the governing equations for the inflation of a flat circular membrane are solved using a variable-step-size-finite difference method and a modified Levenberg-Marquardt algorithm to minimize the difference between the calculated and measured inflation pressure. This will determine the material constants embedded within the models used. For numerical simulation, the lagrangian formulation together with the assumption of the membrane theory is used. Moreover, the influence of the hyperalastic model on the thickness and on the stress distribution in the thermoforming sheet are analysed for ABS and HIPS materials.