Abstract: Closed-form compliance equations are derived for half flexure hinges based on the Castigliano’s second theorem. The compliances of half right circular flexure hinge, half parabolic flexure hinge and half secant flexure hinge are calculated by using these equations. Finite element analysis is performed for verification. The deviation between the results from finite element analysis and these equations is less than 9%. The influence of geometric parameters on compliance is studied. The compliances of several typical flexure hinges are compared.