We study an anisotropic membrane cylindrical shell of an arbitrary shape of transverse section. The thickness of the shell as well as elastic characteristics of its material vary along the contour line of the shell only. Longitudinal ribs discretely support the shell. We obtain an analytic formula for strain-stress state of the shell when tangential loads are applied to its end cross sections or displacements of the end cross sections are specified. We present an analytic solution that is in good agreement with results of finite element analysis.