The problem of boundary feedback stabilization of a Euler-Bernoulli beam with an endmass is considered. Using a method of compact perturbation, the lack of uniform stabilization is proved in the case of a clamped beam with the usual boundary feedbacks applied to the end with the mass. Next, the uniform stabilization when the usual boundary feedbacks are applied to the end without the mass is proved. Also the uniform decay of energy by means of higher-order feedbacks applied to the end with the mass is established.