Flexure hinges are widely employed in miniature and ultra-precision equipments with the development of precision engineering. In this paper, Castigliano's theorem and Labotto quadrature formula are utilized to derive the compliance matrix. An exclusive longitudinal section of corner-filleted flexure hinges is proposed and the curve of the cross-section is expressed by basic design parameters (r0, d, and l) and machining error parameter (η). The influences of parameters are analyzed by the defined evaluation indexes, i.e., rotation capacity, relative flexibility, and relative rotation error, which are used to assess the quality of flexure hinges. The analysis results indicate small d and optimized values of r0, l, and η will improve flexure hinges' performances. The proposed method is verified by finite element method and experiments within a 5% margin of error.