Nanoimprint lithography is a promising technology to produce sub-100 nm scale features on silicon chips. One of key issues in the nanoimprint lithography is how to make uniform contact between the stamp and the substrate on a large area. In this study a rubber membrane unit under substrate is introduced to resolve this problem. Two layers of membrane were designed to consider air flow in the middle of resist on a silicon wafer. The geometry design for accomplishing uniform contact was carried out using finite element analysis. The material modeling of hyperelastic properties of rubber is characterized by the Mooney-Rivlin strain energy functions. Material constants in the strain energy functions are able to be determined via the curve fitting of experimental stress-strain data. Simple tension and equi-biaxial tests were performed to determine the material constants. To evaluate the effects of a rubber membrane unit, nanoimprint lithography process with it was executed. We could confirm that a distinct improvement of uniform contact was shown and air flow problem was solved during the process.