The stress intensity range below which no cyclic plastic deformation at the crack tip and, hence, no fatigue crack propagation occurs is investigated. The emission of dislocations from the crack tip is assumed as mechanism for the dislocation generation. For a mode III crack, a computer simulation is carried out to study the influence of dislocation obstacles. Both the distance between the crack tip and the obstacle and the strength of the obstacle are varied and the characteristic dislocation arrangements are shown.The stress intensity range necessary to return one dislocation to the crack tip is mainly controlled by the critical stress intensity factor sufficient to emit a dislocation. The influence of the obstacles is not very significant.