Abstract: A composite structure of elastic and viscoelastic components in which dynamic loads are effectively damped by transmission through the viscoelastic components. The structure includes a continuous sandwich comprised either of a single elastic layer enclosed by two viscoelastic layers or of a single viscoelastic layer enclosed by two elastic layers such that the sandwich has little stiffness in any intended direction of loading, and two segmented elastic layers having stiffness in a desired loading direction. The segmented layers have alternating segments and gaps and are disposed one on each side of the viscoelastic layer in such a manner that the gaps of one segmented layer overlap the segments of the other segmented layer. Dynamic loads in the loading direction are transmitted back and forth from one segmented layer to the other, through the continuous sandwich layer containing the viscoelastic material, which thereby provides a high degree of damping.