Offshore structural circular tubular members suffering from local dent damage can develop extreme stresses at locations around the dent area. An analytical method for the prediction of elastic stress concentrations in locally damaged circular tubular members is presented. The method is based upon replacing geometric errors with an appropriately chosen load function to be applied to the perfect member for analysis. A simpler approach based upon an axisymmetric analysis, suitable for speedy assessment of the damage effects, is also presented. Axially loaded tubulars containing an idealized dent under stress and displacement-controlled situations are included.