The paper presents the ultimate strength analysis of such a shell raft transmitting vertical loads and moments, subject to perfect lateral restraint of the boundary, under which condition it fails in transverse shear. The analysis applies to the most general case from which results pertaining to simple cases are obtained by suitable substitutions. The theoretical predictions of ultimate strength have been verified by tests conducted on wire-reinforced micro-concrete models of these shell foundations. Together they establish the substantially high values of load factors involved in the traditional design of these shell foundations based on the membrane theory.