In this investigation, a theoretical model for adaptive beam structures with various boundary conditions was developed, and its potential applicability to electrorheological (ER) material based adaptive beams was introduced. The cross-sectional configuration of the beam selected was based on sandwiching a damping material between elastic face plates. The transverse continuous vibration model developed is based on thin plate theory. In the model shear and rotary inertia effects are neglected, and it is assumed that no slipping between the elastic layers and the damping layer occurs. All layers are considered to have the same transverse displacement. The resulting analytical model is able to predict the structural vibration response at any location on the beam surface, and is applicable to generalized sets of boundary conditions. In this study, four different boundary and external excitation conditions were considered, namely; clamped-clamped, clamped-free, clamped-simply supported and simply supported. The transverse vibration response was studied for each boundary condition set. Variations in the mode shapes, natural frequencies, and loss factors as functions of mode number and excitation frequency were analyzed. ER material based adaptive beam semi-active vibration control capabilities were analyzed from the observed model results.