A sophisticated finite strip (FS) for free vibration analysis of pressurised and rotating cylindrical shells is formulated based on Galerkin method. Shell displacements are assumed as products of their axial and circumferential profiles. The circumferential profiles are modelled exactly by using appropriate trigonometric functions. The axial profiles are approximated by suitable shape functions that allow for membrane and bending deformations. As a result, a set of reduced equations of motion is obtained. Consequently, the discretisation is required along the axial coordinate only. The discretisation is carried out using Galerkin method. Finally, a two-node finite strip with a total of eight degrees of freedom (DOF) is formulated: six DOFs for the translational displacements and two DOFs for the rotational displacements. The accuracy of the developed finite strip is proved by comparisons with results obtained by either analytical or finite element (FE) methods in cases of stationary and rotating shells, assuming a variety of boundary conditions. An excellent agreement between the FS and either the exact or the numerical solutions is confirmed.