The tunneling current between two conductors through an intermediate thin‐film insulating barrier in the presence of a magnetic field parallel to the direction of tunneling has been calculated. It is shown that the Fowler—Nordheim tunnel current decreases as the magnetic field is increased and, in certain cases, contains a component which oscillates with a period proportional to 1/H. The oscillations should be observable when the electrons in the material from which the electrons tunnel have a small Fermi energy, a small effective mass, and a long relaxation time. Bismuth, lead telluride, and graphite are examples of materials in which the criteria for observing oscillations are realized.