This paper reports on the development of a dynamic finite element procedure for the simulation of blow molding and thermoforming of thermoplastic hollow parts. The Principle of Virtual Work written herein takes inertia effects into account. The heat-softened parison is assumed to be a nonlinear hyperelastic Mooney-Rivlin membrane and is meshed with classical linear triangular finite elements. We adopt the explicit central differences time integration scheme with the special lumping technique. The mold is divided Into triangular elements and the contact between the parison and the mold is assumed to be sticky. Therefore, contacted degrees of freedom of the parison are fixed on the solid boundary until the end of the simulation. Performances are highly improved by the use of an adaptive mesh refinement procedure based on a geometric criterion for detection and on the simple addition of a node at the mid-side of the longest edge for subdivision. The method is illustrated through some examples of thermoformed and blow-molded parts. Our results are compared with both experimental and numerical results from Literature to validate the present theory.