A second order microstructure theory for the dynamic behaviour of elastic laminates is applied to the problem of a laminated half space, with interfaces normal to the boundary, subjected to harmonically time varying displacement and stress distributions at the boundary. The finite number of modes of the microstructure theory is found to be sufficient to model a uniform normal displacement boundary condition but not a uniform normal stress boundary condition. The solutions yield the constituent displacement and stress distributions both near the boundary and in the far field and permit an assessment of the usefulness of the microstructure theory for such boundary value problems.