A torsional shock absorber dampens rotary shock loading on a well drill string. An outer housing has driven splines on an inner surface. A mandrel is located within the outer housing and has drive splines on an outer surface that fit between the drive splines on the inner surface of the housing. Dampening bars are positioned longitudinally between the splines of the outer housing and the splines of the mandrel to absorb shock from non-uniform torsional loading at the drive interface between the outer housing and the mandrel.