The probability of electron tunneling from a bound to a free state in an alternating electric and a constant magnetic field is calculated in the quasiclassical approximation. It is shown that the magnetic field reduces the probability of electron tunneling. The application of the external magnetic field perpendicular to the electric field reduces the ionization probability at high magnetic fields, when cyclotron resonance frequency becomes larger than reciprocal tunneling time. The increase of electric field frequency to values larger than the same reciprocal tunneling time enhances the influence of magnetic field. (C) 1999 Elsevier Science B.V. All rights reserved.