An analysis is presented for the vibration and stability of an orthotropic circular cylindrical shell subjected to an axial static load by use of the transfer matrix approach. The applicability of the thin‐shell theory is assumed, and the governing equations of free vibration of the shell are written in a matrix differential equation by using the transfer matrix of the shell. Once the matrix has been determined by a solution to the equation, the natural frequencies and the critical loads are calculated numerically in terms of the elements of the matrix for a given set of boundary conditions at the edges. This method is applied to orthotropic circular cylindrical shells simply supported at the edges, and the effects of the length ratio, orthotropy, and axial load on the vibration and stability are studied.