In oil well, the rubber packer often needs to give a certain amount of compression to ensure its outer surface can be stably sealed. For the predicted Mises stress smaller than the actual Mises stress due to soft in single axis compression (SAC) stress prediction by Yeoh (N=3) model, For the sake of more reasonably predict the stress under static compression of rubber packer, the sealing effect evaluation based on the SAC contact stress and Mises stress calculation of rubber packer is given on Yeoh_revised model. On the assumption of Hydrogenated Nitrile-Butadiene rubber (HNBR) is isotropic and incompressible, first, we derived the fitting formula for the three types of constitutive. Simultaneously, the accuracy of three models (Yeoh, Yeoh_revised, Ogden) were evaluated by fit goodness (R2) from three kinds of tensile experiment test. The highest R2 is 0.9771 from Yeoh_revised model, which mergers advantages of another two fitting models, effectively improves the Yeoh model soft characteristic of SAC contact stress. Additionally, on the premise of ensuring the sealing rubber packer contact stress stable, the maximum Mises stress on the inner surface calculated based on Yeoh_revised model is 131.60MPa great than Yeoh model of 104.42MPa, which achieves more accurate in predicting the Mises stress and predicts the possibility of seal failure in advance, also contribute to rubber packer structure optimization that prolong its service life. For the compression amount calculated by the model Yeoh_revised is lower under the same load, which can effectively avoid excessive compression of the rubber packer.