In this work, the problem of the modeling of thermoforming and blow molding processes for viscoelastic sheet are considered. To take account of the enclosed gas volume, responsible for inflation of the thermoplastic membrane (which contributes significantly to the strength and stiffness of a thermoplastic structure), we considered thermodynamic approach to express external work in terms of a closed volume. The pressure load is thus deduced from the thermodynamic law of ideal gases. The viscoelastic behavior of the K-BKZ model is considered. The Lagrangian formulation together with the assumption of the membrane theory is used in the explicit dynamic finite element implementation. The numerical validation is performed by comparing the theoretical bubble free inflation with numerical results. Moreover, the influence of the K-BKZ constitutive model on the thickness and stress distribution in the thermoforming of containers is presented.