A method for analysing the form of dislocation arrays which accommodate misfit at epitaxial interfaces based on the Frank-Bilby expression of the dislocation content of an interface is presented. Emphasis is placed on the deformation of a crystal in the presence of a dislocation array, and ease of formulation through use of an orthogonal reference frame. Several aspects of epitaxial growth are subsequently addressed, including the uniqueness of a dislocation array accommodating a given misfit. In the case of growth on vicinal cubic surfaces, it is shown that dislocations generated to relieve misfit may also lead to misorientation of the overlayer. From experimental measurements of dislocation densities using transmission electron microscopy, it is possible to calculate the state of strain in a metastable misfitting epitaxial layer. When misfit is not isotropic in the interface (such as for silicon or niobium grown on sapphire) it is shown that dislocation line directions may not lie along low index directions in either crystal, a point which is particularly important with regard to studies of interfacial structure by high resolution electron microscopy.