In order to design composite materials with high intrinsic damping, it is essential to understand the effect of volume fraction and morphology (size, shape, and distribution, etc.) of the component phases on the damping behavior. The analytical solutions available to date are concerned with specific morphologies and thus cannot predict the result of a change in the morphology of the component phases even though they can account for volume fraction effects. In this investigation, the finite element method (FEM) has been employed to predict the effect of both the volume fraction and morphology of phases on the damping behavior of epoxy-aluminum composites. Various finite element meshes representing different composite morphologies were made with two-dimensional plate elements. A cantilever beam with an end load applied as a sinusoidal function of time was modeled. The solution consisted of the displacements of the nodes and the stresses in each element for a given time. From this information, the phase lag between the stress and the displacement as well as the local stress and strain distributions were determined.