In this paper, we are concerned with asymptotic stability of a class of Bresse‐type system with three boundary dissipations. The beam has a rigid body attached to its free end. We show that exponential stabilization can be achieved by applying force and moment feedback boundary controls on the shear, longitudinal, and transverse displacement velocities at the point of contact between the mass and the beam. Our method is based on the operator semigroup technique, the multiplier technique, and the contradiction argument of the frequency domain method. Copyright © 2015 John Wiley & Sons, Ltd.