Strained layers are incorporated into many electronic devices and particularly into semiconductor lasers. These strained layers can relax, both elastically and plastically, which often impairs the performance of the device. This thesis presents several methods for calculating elastic strain relaxation: a Fourierseries method for stresses imposed on the surfaces of a rectangular block; a Fourier-integral for stress imposed on the surfaces of an infinite layer; and a Green-function method for the stress field about buried inclusions. The methods are used to calculate the strain distributions in a transmission electron microscopy sample, the relaxation at the end facet of a strained-layer laser, and the strain field about a rectangular buried layer. The effects of the strain relaxation on the optical absorption of the laser facet and the zone-centre band structure of the buried layer are discussed. The equilibrium theory of critical thickness is examined in detail and is shown to make unreasonable predictions for highly strained layers; a modification which corrects this behaviour is suggested. The equilibrium theory equates the line tension of a strain relieving dislocation to the strain energy it relieves in the layer. The additional energy corrections which can be included in the line tension are discussed, together with the failure of the equilibrium theories to reliably predict plastic relaxation in all situations.