Extremum principles are applied to the problem of estimating loads sufficient to cause pronounced plastic yielding in notched bars. The theory is two-dimensional and an ideal plastic-rigid material is assumed. Upper bounds to the constraint factors in pure bending are obtained for deep notches with circular and wedge-shaped roots, and for shallow notches of any shape. The estimates for deep notches are calculated by means of slip-line fields constructed to satisfy all conditions in the plastic region; but since the associated stress distributions in the rigid zones are not examined, it is not known theoretically whether these are complete solutions. A simple method is presented for ascertaining whether the rate of plastic work is positive in a given slip-line field. Experiments are described in which wide bars of copper, stainless steel, and mild steel, deeply notched on one side only with a single wedge-shaped notch, were bent by pure couples applied at each end. The yield-point couples, the surface deformation, and the regions of plastic deformation (revealed by etching bent mild steel specimens) agreed closely with the theory.