A kind of elliptical flexure hinge named deep-notch elliptical flexure hinge was proposed by taking notch width as the length of minor axis and notch deepth as the length of long axis for an ellipse. Based on the bending theory of beam with variable cross-section in material mechanics, the integral formula of the elliptical flexure hinge was deduced by inducing centrifugal angle as the integral variable. By defining an intermediate parameter in the integral formula, more concise analytical equations of compliance, rotation precision and maximum stress of elliptical flexure hinges were deduced to avoid time-consuming numerical integrals. A number of elliptical flexure hinges with different shapes were analyzed by using ANSYS finite element software. The analysis results are coincident with that of analytical formula well. Where, the maximum errors of angular displacement, maximum stress and rotation precision are less than 4%, 5% and 7%, respectively. These data indicate that the analytical equations are correct and also show that deep-notch elliptical hinge is a good choice for high precision transmission.