An intense electron beam travelling axially through a superconducting tube is studied. We show numerically that it is necessary to compensate the space‐charge effect of the electron beam nearly completely in order to focus the beam by means of the superconductor tube. The tube functions as a lens not only for electrons injected parallel to the tube axis but also for electrons having a small initial radial velocity component. Additionally, it is suggested that the simple straight superconducting tube may function as a wiggler for free‐electron lasers. ©1995 American Institute of Physics.