This work investigates the compliance of a novel flexure hinge mechanism for tissue cutting. This hinge is to be used with ultrasonic axial vibration to induce transverse displacement. This transverse motion can aid in reducing tissue cutting force as well as possible target deflection by reducing the parallel tissue cutting force. The finite element method, FEM, is used to evaluate several flexural hinge designs to develop empirical equations for the compliance in the axial, transverse, and rotational directions. To generate appreciable transverse motion from an axially applied ultrasonic vibration an asymmetric flexural hinge is needed. In order to design an asymmetric complaint mechanism to fully take advantage of the transverse cutting motion the compliance with respect to geometry was explored. The ratio of thickness, length, and distance between the hinges were iterated while end loads were applied to derive the compliance equations. The empirical models are presented for each design study. It is shown that the rotational stiffness is the dominating factor of the stiffness matrix. It is also shown that the relationship between the rotational stiffness and the distance between hinges forms a piecewise equation. This is due to notch elements spaced close to each other can be modeled as a lumped element while notch elements spaced further apart need to be independently modeled.