Transmission electron microscopy provides a powerful means of studying compositionally modulated materials. In such materials there is usually a local variation in electron scattering power along with a lattice dilatation wave which both accompany the local composition. The most revealing geometry for studying such materials has the lattice modulation direction lying within the plane of the thin foil. However, shear stresses accompanying the dilatation wave can be significantly relaxed by the presence of the thin foil surfaces, modifying the local atomic displacement field such that it is representative of neither the bulk, nor the free unstressed material. Two pertinent semiconductor examples which we have studied are spinodally decomposed quaternary III–V layers and strainedlayer superlattices of Si/SixGe1−x. We provide experimental evidence demonstrating relaxation in these cases and a simple elasticity model to describe it. Our data and model show a thickness dependence to relaxation and can explain previously reported ‘anomalous’ lattice parameter measurements from a strained-layer superlattice [11]. In this paper we concentrate on the effects of dilatation and relaxation on imaging and diffraction from a strained-layer superlattice.