It is well known that it becomes energetically favourable for misfit dislocations to be introduced into strained epitaxial layers above a certain ‘critical’ layer thickness, hc. To date, theoretical calculations of hc have only been made for cases of isotropie misfit - i.e. cases where the misfit is the same for every direction in the interface. Using a new formulation of the Frank-Bilby equation and the concept of coherency dislocations, it is now possible to treat cases of anisotropie misfit, such as silicon on sapphire (SOS). The method used to obtain the critical thickness is described, and values of hc and equilibrium dislocation density are given for various materials systems.