Vlasov's semi-membrane isotropic shells theory is extended to composite cylindrical shells. The resulting theory can be used to obtain closed-form solutions for the statics and dynamics of composite cylindrical shells. Two versions of the theory are proposed. The range of applicability and the accuracy of the new theory are established via a comparison of natural frequencies calculated by the theory with those obtained by Love's first approximation theory. It is shown that the semi-membrane theory accurately predicts the lowest frequencies of long, composite cyclindrical shells. © 1991.