Uniaxial tension tests were performed on two different thin rubber liner sheets, the silica-filled and the Kevlar-filled EPDM rubber, for the purpose of establishing the constitutive relations via different hyperelasticity models. Due to the fact that the rubber liner sheet can sustain large amount of deformation, over 700 % engineering strain, we used the non-contact, optical technique of digital image correlation to measure local deformation over the sample surface. Three different hyperelastic models were considered for analyzing the experimental measurement, one is the neo-Hookean including the generalized neo-Hookean (GNH), the second is the Rivlin-type models including the special case of Mooney-Rivlin model, and the third is the Ogden model. Model parameters were determined by fitting the hyperelastic model to the experimental data. It was found that the Rivlin model up to the second order and the Ogden model capture the constitutive behavior of both the silica-filled and the Kevlar-filled rubber sheets quite well, while the GNH model can only describe the stress-stretch relation of the Kevlar-filled rubber sheet.