In this study, the non-isothermal viscoelastic simulation of the film casting process was carried out. Low-density polyethylene polymerized by a high-pressure process (LDPE) was used for the simulation. The LDPE exhibited strain hardening in elongational viscosity since it has long chain branching. The Phan-Thien/Tanner model, as a constitutive equation of the viscoelastic fluid, and temperature dependence of the Arrhenius law were employed for the simulation to investigate the effect of viscoelasticity on extrusion drawing, so-called neck-in phenomenon. We developed the theoretical model on the basis of deformation type and force balance of a film to recognize the mechanism of the neck-in phenomenon. It was confirmed from a combination of the simulation results and the theoretical model that neck-in was determined by the ratio of planar to uniaxial elongational viscosity rather than the strain hardening nature of a uniaxial elongational viscosity.