The stress and displacement fields of an edge dislocation that climbs with a uniform velocity are derived. This solution has application for the determination of the stress and displacement field arising from the anomalous edge component of a moving partial dislocation. The climb motion of the anomalous edge component does not involve diffusion of point defects and is not restricted to slow velocities. The self‐energy of a climbing edge dislocation also is determined. It is found that the self‐energy diverges as (1−V2/c2)−1/2, whereVis the dislocation velocity andcis the transverse sound velocity when the dislocation velocity approaches the slow sound velocity. This divergence is not as strong as that of the gliding edge dislocation [which is (1−V2/c2)−3/2].