Electrons traveling through a superconducting tube are studied. Two simple models are proposed to describe the interaction of the magnetic self-field of the electron stream with the superconducting tube. In the first model A, a complete expulsion of the magnetic flux from the superconductor due to the Meissner effect is assumed. On the contrary, a complete flux penetration through vortices is supposed in the second model B. Both models indicate an electron focusing when the space-charge effect is compensated. The focusing length is estimated. For electrons traveling in the vicinity of the tube axis, the focusing length determined according to model A is nearly independent on the distance of the electrons from the tube axis, while the focusing length according to model B increases at increasing distance of the electrons from the tube axis. Similar focusing effects are obtained by a superconducting cone. © 1995 American Institute of Physics.