Nanoimprint lithography (NIL) is an emerging technology enabling cost-effective and high-throughput nanofabrication. To successfully imprint a nano-sized pattern, the process conditions such as temperature, pressure, and time should be appropriately selected. This starts with a clear understanding of polymer material behavior during the NIL process. In this work, the squeezing of thin polymer films into nanocavities during the thermal NIL has been investigated based upon a two-dimensional viscoelastic finite element analysis in order to understand how the process conditions affect a pattern quality. The simulations have been performed within the viscoelastic plateau region and the stress relaxation effect has been taken into account.