The most commonly used beam model for constrained layer damping was developed by Mead and Markus in 1969. Although three displacement variables were used in the model, only two of them were independent. As a result, boundary conditions that are allowed in the Mead-Markus formulation may sometimes be limited. For example, a simple lab setup often consists of a cantilevered base beam with free-free constraining layer. In this case, the axial displacements of the beam and the constrained layer are independent at the cantilevered end. This boundary condition violates the basic assumption of the Mead-Markus model and cannot be described under the Mead-Markus formulation. In this paper, we investigate a modified model that is able to incorporate such boundary conditions by using three independent displacement variables. The modified model is demonstrated on a cantilevered beam with a free-free constrained layer treatment. The frequency response functions were obtained both experimentally and analytically. Our results show that the modified model is able to accurately predict vibration response. An investigation into the frequency response functions of the Mead-Markus model under similar boundary conditions is also reported.