In the present work, motivated by the recent results given in [1,2], we investigate the properties of transverse electric (TE) and transverse magnetic (TM) surface plasmon polariton (SPP) modes which propagate parallel to the azimuthal direction of a cylindrical metal-insulator-metal structure, theoretically. In this way, we use the Maxwell equations with appropriate boundary conditions and derive the dispersion relations of SPP waves for two types of modes, on the basis of a Drude model for the dielectric function of the metals. Then, we study the effects of geometry and insulator thickness on the propagation of SPP modes. In particular, we wish to distinguish the difference in the characters of two different propagating modes, i.e., TE and TM modes.