The motion of pre-existing edge dislocations in an infinite linear elastic body is studied. Motion, is due to a quasi-statically steady-state growing crack. In the model, the dislocations glide if the force on the dislocation exceeds a critical value. Obtained results are changes in dislocation density, the shielding effect on the crack tip and residual stresses. The model is applied to an isotropic material. The residual stress far behind the crack tip is tensile near the crack, decreasing to zero at a certain distance above the crack plane. The indication is that the shielding effect may be considerable