In this paper we present a shear force feedback control method for a single-link flexible robot arm with a revolute joint for which it has been shown that direct bending strain feedback can suppress its vibration. Our primary concern is the stability analysis of the closed-loop equation which has not appeared in the literature. We show the existence of a unique solution and the exponential stability of this solution by doing spectral analysis and estimating the norm of the resolvent operator associated with this equation. Some experiments are also conducted to verify these theoretical developments.