In this paper, the strain and stress field produced by an edge dislocation are expressed by means of continuous dislocation distribution. The stresses inside and outside the core of the edge dislocation are obtained. The dislocation distribution of infinitesimal strength is expressed by crystal defect gauge field, which are calculated under certain gauge condition. In side the core, the stresses are finite when r goes to zero. The singularity of stresses is removed. Finally, the energy of the edge dislocation are calculated.