A recent design concept for millimeter‐wave free‐electron lasers [J. Appl. Phys.60, 521 (1986)] would require the stable propagation of a sheet electron beam through a narrow waveguide channel. Experimental results reported in this article support the feasibility of such a configuration by demonstrating the stable propagation of relativistic sheet electron beams through a narrow waveguide gap (3.2 mm) using focusing by a short‐period electromagnet wiggler. 90% of the electron current in a 100‐keV sheet electron beam was transmitted through a 5‐cm‐long channel with peak wiggler fields of 800 G. Almost 80% of a 400‐keV beam was similarly confined with a 1600‐G wiggler field. The data were consistent with single electron trajectory models, indicating that space‐charge effects were minimal. No evidence of beam breakup or filamentation instabilities was observed.