Abstract: In this paper,it is shown that,by introducing a function of displacement,the governing equations in ref,1 for the classical laminate theory of orthotropic la urinated cylindrical shell can be reduced to one equation in terms of displacement function,On the basis of such a differential equation and by extending W.Nowacki's method,an analytical solution to the problem of buckling of a laminated composite cylin drical shell with longitudinal ribs is given.The reliability of the function of displacement is checked by calculating some examples in which all the parameters refered to the ribs are neglected.T he calculated results of the critical loads are exactly equal to those in ref,1,which shows that the derived displacement function is correct.The calculated results of the examples also show that the influence of ribs obviously exists,generally,the values of the critical load for laminated composite cylindrical shells without ribs are lower than the corresponding ones for cylindrical shells with reinforced longitudinal ribs.