An analysis of the stability of the kink mode of a relativistic charged‐particle beam propagating in a toroidally confined plasma is presented. The essential feature is the treatment of the beam as a distinct component of the system having finite velocity and inertia in addition to its current. To simplify the analysis, the plasma background is assumed to be a pressureless, uniform fluid obeying the laws of perfect magnetohydrodynamics while the beam is treated as a cold, rigid body. To simulate toroidal geometry, periodic boundary conditions are imposed in the axial direction of a straight, cylindrical volume. The walls of the cylinder have perfect conductivity. A strong solenoidal field is externally imposed, but the beam is the only source of the poloidal field. It is found that a modification of the stability condition of Kruskal and Shafranov applies; the onset of instability corresponds to the appearance of closed particle orbits rather than the more severe condition of closed field lines. The maximum rotational transform consistent with stability is&igr;/ 2&pgr; = 1 + (&bgr;z &ggr;mc2) / (e R 0 Bz).