A continuum theory for elastic wave propagation in three-dimensional composite materials with imperfect bonding between the phases is presented. The theory provides the dispersion relations for harmonic wave propagation, and the dynamic response of the composite to impulsive loadings. Long-fiber and periodically bilaminated composites are obtained by a proper selection of some geometrical parameters. Furthermore, perfect contact, perfect lubrication and complete debonding of the constituents are obtained as special cases. The effects of periodic distribution of cracks in solids, and of damage in composite laminates on propagating elastic waves are presented.