Representative production cross‐sections for bremsstrahlung, which constitutes an unavoidable spectral background in an X‐ray analysis using electron beam excitation, have been calculated as a function of target and angle for incident electrons in the energy range 0.2—10 MeV. These values, used in conjunction with the corresponding K X‐ray production cross‐sections and non‐fundamental experimental variables particular to each laboratory (detector resolution and ambient background), determine the feasibility of a K X‐ray analysis by direct electron beam excitation, and permit the evaluation of an ideal detection limit. Copyright © 1987 John Wiley & Sons, Ltd.