The general theories of thin elastic cylindrical shells as derived by Love and Novozhilov are compared and then used in a simple binary flutter analysis which permits the existence of both axial and circumferential waves of deformation. Linear piston theory has been used and the results obtained indicate that the axi-symmetric mode of deformation is the most critical. Comparisons are then made with other published results and apparent inconsistencies in those papers are found to arise from certain assumptions made in the deformation equations used. In a further axisymmetric mode analysis the use of a travelling wave form of radial deflection is shown to give similar results as standing wave forms when applied to a shell of finite length.