The aeroelastic stability of a flexible elevator aerodynamic balance horn in a shear layer wake flow is investigated. The study was motivated by a pilot report of a “buzzing” observed on his aircraft's elevator aerodynamic horn balances under normal operating cruise conditions. Based on hot wire mean wake flow measurements, a “cosine”-type math model and a “Gaussian error function” math model are developed for the shear layer flow field. The resulting nonlinear dynamical equations of notion are evaluated for stability through the analysis of singular points in the phase plane. A limit cycle oscillation is found to occur under trim conditions where the elevator balance horn unports. Compliance with an existing civil aviation requirement for eliminating aeroelastic divergence on controls with aerodynamic horn overhang is recommended pending further study of the galloping phenomenon for the development of design guidelines.