•A Transfer Matrix Method for infinite multilayered cylinders has been developed.•Interactions with internal and external fluid media are modelled analytically.•Diffuse acoustic field excitation has been considered.•The method was validated by comparison with analytical solutions.•The acoustic transmission through heterogeneous cylinders has been predicted. This paper discusses the use of a Transfer Matrix (TM) method for predicting the acoustic behavior of infinite cylinders consisting of a generic arrangement of homogeneous and heterogeneous periodic layers of various nature (fluid, solid, poroelastic). A through-radius TM is derived for a layer characterized by cylindrical periodicity by manipulating the dynamic stiffness matrix related to a finite element model of a unit cell. The proposed technique is equally appealing for homogeneous layers since few elements are needed in this case. In such a framework, different layers can be combined to form multilayered systems and the related acoustic radiation or transmission due to an external plane wave or a diffuse acoustic field can be assessed. The proposed approach is validated in case of cylinders consisting of homogeneous layers by comparison with alternative approaches. In order to demonstrate the usefulness of the approach, the sound transmission through a cylindrical structure with resonators is presented.