Nanoimprint lithography (NIL) is a next generation technology for fabrication of micrometer and nanometer scale patterns. There have been considerable attentions on NIL due to its potential abilities that enable cost-effective and high-throughput nanofabrication to the display device and semiconductor industry. To successfully imprint a nanosized pattern with the thermal NIL, the process conditions such as temperature and pressure should be appropriately selected. This starts with a clear understanding of polymer material behavior during the thermal NIL process. In this paper, a filling process of the polymer resist into nanometer scale cavities during the thermal NIL at the temperature range, where the polymer resist shows the viscoelastic behaviors with consideration of stress relaxation effect of the polymer. In the simulation, the filling process and the residual layer formation are numerically investigated. And the effects of pressure and temperature on NIL process, specially the residual layer formation are discussed.