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Hertz contact stress theory is the classic theory,it involves more complicated calculation process. In this paper,through theoretical analysis and numerical fitting,a relationship of the contact curvature function and contact elliptical rate was found,that is ln（ 1 / e） = 0. 224[ln[1 / F（ ρ） ]^{1. 407}. Then,a elliptical rate is calculated directly by contacting curvature function,no longer need to process the look-up table and interpolation calculation that would be a kind of trouble and not accurate. At the same time,the stress states at a key point of contact body are found by elastic analysis results,and a method of the yield strength checking is estimated. It could bring convenience in engineering application.