Abstract: The unique low temperature environment of polar drilling hardens rubber gradually to the point of even vitrifying it so it loses its original elasticity. This can easily cause the sealing failure of key drilling equipment, such as mud pump and BOP, which affects normal production and brings about potential safety risks. Therefore, it is necessary to optimize the rubber sealing materials used in the key equipment for polar drilling. According to the National Standards GB/T 528—2009 and GB/T 7759.2—2014, the rubber materials were subjected to uniaxial tension and compression permanent deformation tests at the temperature of 20～–50 °C, and the test data and the hyper-elastic constitutive models of several common rubbers were fitted to obtain the model parameters, so as to analyze the applicability of these constitutive models under low temperature conditions. The sealing performance of rubber O-ring at –45 °C was simulated and analyzed by using ABAQUS finite element software, and found the location of the seal failure which is easy to occur at low temperature. According to the analysis, Polynomial (N=2) model and Ogden (N=3) model can accurately describe the mechanical properties of rubber under low temperature and small deformation conditions. Silicone rubber, gas rubber and nitrile rubber can still maintain superior sealing performance under polar environments (–45 °C), so they can be used as the rubber sealing materials for key equipment of polar drilling. The analysis of rubber super-elastic constitutive model at low temperature and the optimization of rubber sealing materials can provide theoretical guidance and support for the future polar drilling of China.