This paper presents the design of a flexure-based mount allowing adjustment in three rotational degrees of freedom (DOFs) through high-precision set-screw actuators. The requirements of the application called for small but controlled angular adjustments for mounting a cantilevered beam. The proposed design is based on an array of parallel beams to provide sufficiently high stiffness in the translational directions while allowing angular adjustment through the actuators. A simplified physical model in combination with standard beam theory was applied to estimate the deflection profile and maximum stresses in the beams. A finite element model was built to calculate the stresses and beam profiles for scenarios in which the flexure is simultaneously actuated in more than one DOF.