The characteristics of the plastic enclave at the tip of a crack in a medium subjected to stress are investigated by means of a dislocation model. A model in which dislocations can glide along a plane coplanar with the crack has previously been given by Bilby, CottreU and Swinden (1), and it is the purpose of this work to extend these authors' results to more general situations. We first of all consider the case of a single slip plane at the crack tip which is inclined to the plane of the crack, and develop an approximation technique for solving the equations of equilibrium of the dislocations. This yields the size of the plastic zone, the density of dislocations and the plastic displacement at the crack tip as explicit functions of the crack-length, applied stress, angle between crack and slip--plane and yield stress and elastic modulus of the medium. These functions become particularly simple for either low or high stresses. A more difficult problem is that in which slip can occur on two different slip--planes at the crack-tip. The same approximation method can be used, but the results are no longer expressible in terms of elementary functions. A computer program has been used to calculate numerical solutions in some cases and in one case to evaluate higher approximations to the solution.