Nonlinear bending deformations of generally laminated circular cylindrical shells subjected to an axisymmetric radial pressure, axial loading, and torsion are considered. Deformations of such shells are axisymmetric, i.e., while cross-sections can rotate about the shell axis, they remain circular and all derivatives with respect to the circumferential coordinate are equal to zero. In this case a nonlinear term is included into the axial strain only. Excluding this strain from the equilibrium equations, one can reduce the analysis to integration of a system of linear differential equations. In the first part of the paper the solution based on Love's first approximation and Donnell's theories is shown for thin shells. While out-of-surface boundary conditions can be arbitrary, several combinations of in-surface conditions are discussed. The second part of the paper outlines the approach to the solution for shear-deformable geometrically nonlinear shells. First-order shear-deformation theory is used in the analysis. The approach is based on exclusion of the nonlinear term (axial strain) and subsequent solution of linear differential equations of equilibrium by the operational method. This approach can be also used for analysis of thin, generally laminated cylindrical shells.