Stress and displacement fields in bipolar coordinates are derived and expressed in terms of a stress function, the compatibility equation becoming the governing equation of the problem. Under the assumption of single-valuedness of stress, a general form of stress function is given composed of the fundamental part used by Koehler and an auxiliary part which helps to satisfy the boundary conditions. The total stress function yields the desired discontinuity of displacement corresponding to the edge dislocation. A general expression for the stress field thus results which can be applied to particular problems (eccentric dislocation in a circular cylinder, dislocation in a half space, two unlike dislocations in an infinite space) by merely adjusting the values of coordinates corresponding to the boundaries. Numerical examples are solved for all three problems and graphs are given illustrating the stress fields.