This paper investigates the vibration suppression and energy harvesting problems of elastically supported beams with Nonlinear Energy Sink and Giant Magnetostrictive Materials (NES-GMM). Based on Hamilton’s principle, Galerkin method, the governing equations of the coupled beam, NES-GMM system are derived. The response of the beam under harmonic excitation is numerically solved by the fourthorder Runge-Kutta method. The vibration suppression effect of NES-GMM on the beam was analyzed in both time and frequency domains. A detailed numerical study is carried out to investigate the effects of the structural parameters on the vibration suppression and energy harvesting of the NES-GMM. The results indicate that the NES-GMM system is highly effective in suppressing multimodal transverse vibrations of elastically supported beams under harmonic excitation, showcasing a notable degree of independence in its vibration suppression and energy harvesting capabilities.