The thesis describes a theoretical and experimental investigation into the ultimate flexural strength of uniformly loaded two-way rectangular concrete slabs (reinforced and unreinforced) with membrane action induced by restraint against lateral displacement at the boundaries. The experimental part of the programme involved the making up and testing of 45 concrete slabs. In addition, the results of 22 slabs tested by other investigators are analysed. The investigation is divided into four main parts. Firstly, a yield-line theory incorporating a rigid-plastic strip approximation is developed which defines the loaddeflection curve at and after the ultimate flexural load for slabs with rigid boundaries during the compressive membrane action stage. Cases of boundary restraints which produce compressive membrane action in either one or two directions are considered and the accuracy of approximate yield-line patterns are investigated. On the basis of an empirical value~first for the width of the yield bands and thence for the central deflection at the ultimateload~expressions are obtained for the ultimate flexural strength of slabs which compare well with results obtained from slabs tested under short-term loading in very stiff surrounding frames. Secondly, the theory is generalized to take into account the effects of axial strains in the slab and of small lateral displacements at the boundaries,in order that the etfects of long-term loading and elastic boundary restraints may be included •. The theory is checked against test results obtained :f'rom slabs tested under periods of sustained loading. It is shown that axial strains and small lateral displacements at the boundaries can significantly reduce the compressive membrane action, especially in the case of thin slabs. Thirdly, the behaviour of a slab as a tensile membrane at large deflections beyond that at the ultimate :f'lexural load is examined. A theory is developed to de:f'ine the loaddeflection characteristics ,assuming that the reinforcement acts as a plastic membrane. It is shown that heavily reinforced slabs can carry loads by tensile membrane action which exceed the ultimate :f'lexural load. Finally, the laterally sti:f'fness and strength required 01' surrounding beams and panels of slab and beam floors in order to entorce membrane action in interior panels is investigated. Results obtained from tests on the interior panels of 9 panel floors are analysed and show good agreement with the theory. An appendix containing some results obtained by the conventional Johansents yield-line theory is also included