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The influence on the crack growth rate on a microstrucurally short edgecrack, subjected to fatigue loading, due to changes in crack length, distance to grainboundaries and applied load, is investigated. The crack is assumed to grow in a singleshear mechanism due to nucleation, glide and annihilation of dislocations alongpreferred slip planes in the material. The geometry is modelled by distributeddislocation dipole elements in a boundary element approach under quasi-static andplane strain conditions. The evolving plasticity is described by discrete dislocationssituated along one single slip plane in front of the crack, coinciding with the crackdirection.