In this work, we consider a nonisothermal finite-element analysis approach using an explicit dynamic procedure for the forming of a polyethylene terephthalate (PET) sheet subjected to air-flow loading. The dynamic pressure load is thus deduced from the van der Waals equation of state. The effect of the radiative-conduction heat transfer during the reheating stage, the stress-deformation behavior during the incomplete forming stage, and the solidification during the cooling stage are simulated. The viscohyperelastic behavior of the Christensen–Yang-like model is considered. The Lagrangian formulation, together with the assumption of the membrane shell theory, is used. The viscohyperelastic model is validated with the equibiaxial stretching tests. Also, temperature validation is performed by comparing the computed, the theoretical, and the experimental temperature profiles obtained from measuring the inside and outside PET sheet surface. An example of thermoforming a PET part is presented. In this example, the influence of the air-flow on the thickness and the stress distribution is presented. POLYM. ENG. SCI., 47: 2129–2144, 2007. Š 2007 Society of Plastics Engineers