A mixed variables transfer function is presented for analyzing the stability of orthotropic cylindrical shells and stepped cylindrical shells. First, displacement variables are expanded in trigonometric series of circumferential coordinate. Flügge thin shell theory and variational principle are adopted to obtain governing equations and find dual force variables. Consequently, governing equations are written in the form of mixed variables. State-space equation of the system is established by defining mixed state variables. Then, by transfer function method, closed-formed solutions for buckling problems of cylindrical shells under axial compression with arbitrary axisymmetric boundary conditions are obtained. Finally, solutions for buckling problems of stepped cylindrical shells are obtained by enforcing displacement continuity and force balance. Driving process of analytical solutions show that it is very convenient for introducing boundary conditions and solving the buckling problems of stepped cylindrical shells in this method. Numerical results validate this method.