Rock wedges in the roofs of underground excavations may be wholly or partly self-supporting due to the mobilization of shear resistance on discontinuities bounding such wedges. The extent of the mobilization, which occurs as the wedge deforms, is markedly influenced by the magnitude of the stress field tangential to the opening and the relative stiffness of the intact rock and the shear and normal stiffnesses of the discontinuities. Analytical and numerical models are described for determining the upper and lower bounds of the failure loads for two-dimensional asymmetric and symmetric rock wedges. Experiments conducted on physical models indicate that the stability of rock wedges may be substantially reduced by loosening and that the analytical solutions may overestimate the load necessary to cause failure.Keywords: rock wedge stability,in situstresses, joint stiffness.