Composition modulations in defect‐free crystalline materials are generally accompanied by a lattice distortion where unit cell dimensions are not characteristic of the local composition. The distortion originates from the constraint that the interatomic spacings perpendicular to the modulation direction be commensurate from one layer to the next. Thus there is an internal stress field set up in the material which attempts to suppress unit cell expansions and contractions in these perpendicular directions. A well‐known example is the tetragonal distortion observed in bulk, cubic strained layer superlattices, and spinodally decomposed alloys. However, it is frequently overlooked that these stresses can be significantly relaxed near surfaces of the bulk material, particularly those surfaces lying perpendicular to the modulation direction. This relaxation can be a dominating effect in materials which have been thinned in cross section for study by TEM. Lattice plane bending near the specimen surfaces can cause strong diffraction contrasts, and the local lattice spacings are representative of neither the bulk, tetragonally distorted material, nor the unstressed material. In this paper we discuss how this important, and oft‐neglected relaxation affects TEM bright‐field and dark‐field image contrasts, high resolution lattice images, and interpretation of selected area diffraction data. We also derive expressions, relevant for all sample thicknesses, describing the relaxation strain field in cubic anisotropic materials, thinned perpendicularly to the modulation direction. The results are discussed in the context of two classes of modulated materials, namely spinodally‐decomposed InGaAsP alloys and GeSi/Si strained layer superlattices.