The development of the stiffness and consistent mass matrices for a finite cylindrical shell element is reported. The derivation of these matrices is based upon linear behavior and thin-shell assumptions. Expressing the assumed displacement state over the middle surface of the cylindrical shell element as products of one-dimensional, first-order Hermite interpolation formulas, it is possible to insure that the displacement state for the assembled set of cylindrical elements is geometrically admissible. Mono tonic convergence of the total potential energy is therefore assured as the modeling is successively refined, since the assumed displacement pattern satisfies the admissibility requirements in the statement of the principle of minimum potential energy. A numerical example is included to demonstrate the effectiveness of this cylindrical shell discrete element.