Abstract We study the Landau damping for electromagnetic waves in a inhomogeneous cylindrical plasma in the presence of a strong axial magnetic field. For this task we use the kinetic theory for plasmas. This kind of phenomena can not be studied using only macroscopic fluid models. The results of our work can be relevant to identify the behavior of different electromagnetic normal modes propagating through the system, in particular, the energy of the damped modes can be transferred to the plasma particles through resonant interactions and according to the mode polarization can be used in modern particle accelerators based in plasmas.