A slab with a circular cutout is subjected to stresses in the plane of the slab. The cutout has removed material which would have participated in carrying the load; hence the slab with cutout will fail under the application of stresses which the complete slab could have supported. In order to eliminate at least part of this weakening, the slab with cutout may be reinforced by the addition of material about the cutout. Such a reinforcement may be designed in any shape. The paper is concerned with extending the results of Weiss, Prager, and Hodge (1) for a cylindrical reinforcement to a reinforcement of arbitrary shape. In particular, a method will be described for the determination of a lower bound on the collapse load for a slab with circular cutout and a general reinforcement.