This paper deals with the vibration analysis of a circular cylindrical shell having partially mixed constrained boundary conditions on both ends. the problems are treated by means of the weighted residual method. In the method by which we determine a solution satisfying all boundary conditions by the superposition of some functions provided for the governing differential equation of motion, we must deal with dynamical conditions as well as constrained boundary ones. Those displacements and the corresponding dynamical boundary conditions are expanded to Fourier series. The equations of free vibration of a circular cylindrical shell are based on Flugge's theory. In this method, we denote a general treatment of calculations for any set of the partially mixed constraints on both ends of the shell.