The properties of differentially rotating, completely degenerate sections of infinite cylinders are examined. Their construction is simple, with variables depending only on the radial cylindrical coordinate. They are found to possess important characteristics which qualitatively resemble much more complicated two‐dimensional models of differentially rotating degenerate stars: (1) an analog of the Chandrasekhar limit; (2) a limit to uniform rotation imposed by centrifugal breakup; (3) massive, differentially rotating structures of moderate radius can be constructed; and (4) models obey the Solberg–Ho/iland criterion for stability of the rotation field and appear to be stable against inverse beta decay and general relativistic collapse. These characteristics combined with the simplicity of construction make these models useful in the study of the structure and evolution of differentially rotating stars.