The filamentation instability of an intense electron beam propagating through a collisional plasma is examined. The effects of the transverse energy and of the pinch force (self‐pinch as well as an applied magnetic field) are included. It is assumed that the characteristic perpendicular wavelength of the perturbations is much less than the beam radius. The stability analysis is carried out for the beam electron distribution in which all beam electrons have the same energy in rotating frames and a Lorentzian distribution in axial canonical momentum. From the stability analysis, it is found that the transverse energy and the pinch force strongly stabilize the instability. Moreover, the axial momentum spread plays a major stabilizing role.