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This paper presents a means for obtaining both the stress and displacement states which appear in thick, circular, cylindrical shells under arbitrary load and boundary conditions. The governing differential equations and the associated boundary conditions are obtained by utilizing Reissner’s variational principle [6], the assumed form of the stress state containing, in addition to terms corresponding to conventional membrane and bending stress resultants, supplementary sets of self-equilibrating stress resultants. Comparison of results obtained from known elasticity solutions shows that the present theory accurately yields solutions for shells with radius-thickness ratios of the order of 3.0. Numerically computed here, for comparison purposes, is the axisymmetric, periodically spaced, band load problem of Klosner and Levine.