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Within the continuum dislocation theory the asymptotic analysis of the plane strain crack problem for a single crystal having only one active slip system on each half-plane is provided. The results of this asymptotic analysis show that the square root stress singularity remains valid during the plastic deformation, while the dislocation density is proportional to the stress intensity factor and distributed as the square root of the distance from the crack tip. The analytical solution for the angular distribution of the dislocation density is found.Dislocations appear to reduce energy of crystals. For crystals with cracks the high stress concentration near the crack tip causes also high energy of crystals in that region. It is therefore natural to expect that, when the load is sufficiently large, dislocations nucleate near the crack tip to reduce the stress level and by this also the energy of crystals. It is then crucial to have the correct perception of how dislocations nucleate near the crack tip. Up to now, the commonly accepted point of view is that dislocations nucleate directly at the crack tip and then glide away from it under the Peach-Koehler force [1,2]. However, the analysis of crack problems reveals that the resolved shear stress is large not only at the crack tip, but also in its neighborhood.