Nanoimprinting has been recognized as a highly potential method of volume production for nanoscale devices. In the nanoimprinting process, the filling process of the mold cavity plays a key role in determining the productivity of the nanoimprinting process and the quality of the final imprint product. A defective filling of the mold affects the uniformity, precision, and throughput of the imprint. The mold filling is subjected to the applied imprinting pressure and temperature, repetitive mold use, mold sticking, or factors regarding mold features. It involves physical contact between the mold and the polymer layer on the substrate surface; thus, how the polymer fills up the cavity is of major interest and is vital in pattern transfer. The proposed study employs a finite element model for the single mold cavity to simulate the nanoimprint process. The mold is assumed to be a linear elastic body and the polymer preheated above its glass transition temperature is considered to be nonlinear elastic, described by the Mooney-Rivlin model. The numerical model is able to predict the mold filling at any nanoimprint stage and the mold cavity with various aspect ratios. To study the effects of pattern density and contact friction existing between the mold and polymer during the mold filling of the nanoimprinting process, an imprint mold with mixed pattern density is simulated and a sensitivity analysis of a contact friction coefficient on the mold filling is performed. Both the cavity feature and pattern density have significant effects on mold filling of the nanoimprinting process, while the contact friction coefficient has a mild effect. The obtained results support the development of a process recipe and automatic large-scale industrial production for nanoimprinting.