Nanoimprint lithography (NIL) is an emerging technology enabling cost effective and high throughput nanofabrication. To successfully imprint a nanometer scale patterns, the understanding of the mechanism in nanoimprint forming is essential. In this paper, a numerical analysis of polymer flow in thermal NIL was performed. First, a finite element model of the periodic mold structure with prescribed boundary conditions was established. Then, the volume of fluid (VOF) and grid deformation method were utilized to calculate the free surfaces of the polymer flow based on an Eulerian grid system. From the simulation, the velocity fields and the imprinting pressure for constant imprinting velocity in thermal NIL were obtained. The velocity field is significant because it can directly describe the mode of the polymer deformation, which is the key role to determine the mechanism of nanoimprint forming. Effects of different mold shapes and various thicknesses of polymer resist were also investigated.