Abstract: Based on the governing equation of vibration of a kind of cylindrical shells written in a matrix differential equation of the first order,a new matrix method is presented for steady state vibration analysis of a non-circular cylindrical shell simply supported at two ends and circumferentially stiffened by rings under harmonic pressure.Its difference from the existing works by Yamada and Irie is that the matrix differential equation is solved by using the extended homogeneous capacity precision integration approach rather than the Runge-Kutta-Gill integration method.The transfer matrix can easily be determined by a high precision integration scheme.In addition,besides the normal interacting forces,which were commonly adopted by researchers before,the tangential interacting forces between the cylindrical shell and the rings are considered at the same time by means of the Dirac-δ function.The effects of the exciting frequencies on displacements and stresses responses have been investigated.Numerical results show that the proposed method is more efficient than the above mentioned method.