We solve the linear problem of the density response of a neutral or ionospheric layer structure of arbitrary density profile to gravity wave perturbations in the background atmosphere. It is shown that the density response of the bottomside of the structure is of larger amplitude than the topside, whereas the general magnitude of the density response depends on the relative sharpness of the layer density gradient in comparison to the gradient of the quiescent background atmosphere. The sharper the layer gradient, the larger the layer density response. Interpretation and application of our results to the ozone and atomic oxygen layers, the sporadic-E layer and to the D and E regions of the ionosphere are discussed.