An elastic continuum model is used to investigate distributions of misfit dislocations in a capped layer structure. Effects of the free surface at the top of the cap and of interactions between dislocations have been rigorously incorporated, making the study applicable to structures with caps of arbitrary thickness and to the process of strain relaxation in layers already containing misfit dislocations. Two dislocation types are considered in detail: single dislocations (singles) residing at the lower interface, between the strained layer and the substrate, and dislocation dipoles, i.e., pairs of parallel dislocations with opposite Burgers vectors, one at the lower interface and the other at the upper interface, between the strained layer and the cap. Although singles cause unwanted long‐range distortion in the cap, which is not caused by dipoles, dipoles give rise to increased localised distortion, due to the presence of the additional dislocation, at the upper interface. Hence singles and dipoles compete as misfit dislocation types in capped layers, with the dominant type being determined by the parameters of the layer structure. It is demonstrated that interactions between dislocations are crucial, and that experimental observations cannot be explained by consideration of an isolated single or dipole. Interactions between singles in an array at the lower interface result in a buildup of strain energy in the cap. The rapidity of this buildup with dislocation density demands a transition from relaxation by singles to relaxation by arrays of dipoles; such a transition would not be predicted by a consideration of isolated singles or dipoles. Energy evaluations are performed to incorporate such interactions between dislocations while providing a sequential view of strain relaxation, with singles and dipoles entering the structure one at a time. It is thus demonstrated that a mixture of singles and dipoles is expected in many capped layers of practical interest. An example calculation predicts a mixture that is consistent with experimental observation.