The monolithic flexible joint is introduced as a novel component of inertial guidance instrument. The angular stiffness of the joint is investigated by employing theory of flexure hinges considering the key part of the joint is a variation of the common circular flexure hinge. Closed-form equation is formulated to unify the typical angular stiffness equations developed by other authors in terms of the circular hinge, and the main variables of the formulation are also discussed. Finite element models of the monolithic joint are built to confirm the analytical model predictions. A measuring system controlled by computer is also developed to evaluate the angular stiffness of the monolithic flexible joint. Checked against finite element analysis and experimental measurement data, the analytical model predictions are within 7% error margins. The study results indicate that the angular stiffness is more sensitive to the minimal thickness of hinge and less sensitive to the notch angle and the oblique angle of hinge.