In this paper, the strain and stress fields produced by the dislocation are analysed by means of continuous dislocation distribution. The dislocation distribution inside the core is expressed by the dislocation gauge fields which are calculated under certain gauge condition. The stresses inside and outside the core of a screw dislocation are obtained. Outside the core, the stresses are the same as that of Volterra dislocation, but inside the core, the stresses of the screw dislocation approach zero when ρ goes to zero. Finally, the energy of the screw dislocation is calculated.