Based on the principle of elliptic gear transmission, this paper deduced the calculation formula of elliptic gear contact strength and flexural strength; By using MATLAB software, the paper obtained the contact stress and tooth root bending stress with variable driving gear rotation angle, and the influence of the eccentricity of the ellipse gear on the tooth contact force and tooth root bending stress; It has been conducted that the comparisonsbetween the present elliptic gear and ordinary cylindrical gear by using an parabolic interpolation method to obtain the maximum strength stress relationship; Finally, the finite element model of contact stress of elliptical gears has been established, and the correctness of the calculation theory of elliptical gears was verified.