Plasticity models for shear problems in structural concrete are often based on the assumption of plane stress conditions. This assumption is not valid for confined members such as columns and piles with circular cross-section and shear reinforced with hoops. The confining pressure provided by the hoops may allow a triaxial state of stress to develop. In this paper, the confinement effect is utilised to develop plastic solutions for the maximum shear capacity of circular members. Coinciding upper-and lower-bound solutions are presented. It is shown that confined circular members are able to carry shear stresses which exceed the upper limit imposed on rectangular members in plane stress conditions. The derived solutions are compared with results of a recently conducted test series. Good agreement has been found.