Based on viscoelastic fluid mechanics, this paper presents a simulation model of the flow behaviour of thin polymer film during nanoimprint lithography (NIL). The polymer is imprinted at a constant temperature of 180oC and at a constant imprint speed of 100nm/s by using a tool with a single convex feature of 100 nm in width and 500 nm in height. At the imprint beginning, only a very limited area adjacent to the tool top is affected by the imprint, but subjects to a sudden change of pressure. With the imprint process forward, the wave-like polymer front and the trumpet-shaped profile are predicted to travel out from the imprint patterns. When the tool base intimately contacts the polymer film, another sudden change of the pressure occurs in the area under the interface between the polymer surface and the tool base. These results are of significance to understand the flow behaviour of NIL.