A dispersion relation concerning the stability of the resistive wall modes within a multimode cylindrical analytical model is presented. This paper generalizes the Fitzpatrick–Aydemir model (Fitzpatrick R and Aydemir A Y 1996 Nucl. Fusion1 11) in the presence of an unlimited number of neighboring modes for a tokamak plasma column surrounded by a resistive shell and a feedback system consisting of a number of detector and active feedback coils. The model is applied to the HBT-EP tokamak (Cates C et al 2000 Phys. Plasmas7 3133) with its peculiar feedback system disposal. Finally, an analytical dispersion relation is obtained that can be solved by using a simple MATLAB code.