We numerically investigated the deformation of a viscoelastic polymethyl methacrylene (PMMA) resist into which a rigid SiO2 stamp with a rectangular line pattern had been imprinted for thermal nano-imprint lithography (NIL). The stress distribution in the polymer resist during the molding process was calculated by using a finite element method (FEM) for a detailed analysis of the deformation behavior. Our simulation results exhibited an asymmetric von Mises stress distribution for the polymer around the external line which was due to the squeezing flow under the flat space. The stress seemed to be concentrated at the sidewall close to the centerline of the whole structure. Our simulation revealed that a micro gap was formed between the replicated structure and the outer wall of the mold.