Understanding how the deformation history affects the retraction dynamics of viscoelastic liquid films can provide a tool to design materials. In this paper, we investigate the stretching and retraction of circular viscoelastic liquid films through finite element numerical simulations. We consider a discoid domain made of a viscoelastic liquid. Its central hole is first ‘closed’ and then released, being left free to open under the effect of inertial, surface, viscous, and elastic forces. We perform a parametric study of film retraction, aiming at understanding the effects of the physical and operating parameters on it. In particular, we consider different viscoelastic constitutive equations, namely, Oldroyd-B, Giesekus (Gsk), and Phan Thien-Tanner (PTT) models, and different values of the film initial thickness. For each liquid and geometry, we investigate the effects of the film stretching rate and of liquid inertia, elasticity, and flow-dependent viscosity on the dynamics of the hole opening.