A new model of beam dynamics is presented for treating the resistive hose instability in intense, self‐pinched electron or ion beams. The beam is modeled as a superposition of rigid, independently moving components with different radii. This multicomponent model exhibits the localized resonances and other analytic properties of a Vlasov treatment. The new model is used to calculate the eigenfunctions and the dispersion relation for hose instability of an axially uniform beam propagating in a medium of specified conductivity profile with any specified return current. Wave growth is found to be significantly increased by return current or by a narrow conductivity profile. The results are compared to those of earlier models.