<p>This paper presents an analysis of the ball vibration absorber (BVA) to mitigate the vortex-induced vibration of a structure with elastic support. A phenomenological model consisting of three mutually coupled second-order nonlinear ODEs is developed to represent the primary structure, the BVA and the wake. Using the Harmonic Balance Method and pseudo-arc length continuation, the behaviour of the system is thoroughly analysed, revealing regions of multiple stable and unstable solutions, jump phenomena, and both stationary and non-stationary responses. Key design and coupling parameters are explored, and it is shown that the BVA effectively attenuates structural vibration, especially at low to moderate amplitudes, where the lock-in regime is split into two distinct resonant zones with reduced vibration. In these scenarios, it presents a practical, low-maintenance alternative to more complex solutions such as nonlinear energy sinks.</p>