Abstract: We follow a variational approach to derive the boundary value problem which models a constrained layer beam. When certain energy terms are ignored, this becomes a generalization of the well known Mead-Markus model [D.J. Mead and S. Markus, "The forced vibration of a three-layer, damped sandwich beam with arbitrary boundary conditions", Journal of Sound and Vibration 10 (1969), 163--175]. We prove well-posedness on an appropriate energy state space. Then we study the effect of introducing damping into the middle layer of the structure, and determine the optimal damping as a function of the other material parameters.