A Monte Carlo approach is used in conjunction with the variational method to calculate quasi-bound levels in arbitrary quantum wells in the presence of transverse electric field. This approach is expected to be superior to the conventional variational approach since the results do not depend upon the choice of any starting wave solution. The technique is applied to Al0.3Ga0.7AS/GaAs quantum wells. The shift in the ground state level energies is calculated, along with the tunneling rates for the electrons and holes. We find that the tunneling rates are very sensitive to the band edge discontinuity distribution and to the barrier width in the case of multiquantum wells. The exciton binding energy is also calculated. Due to high tunneling rates at high electric fields, the photoluminescence is expected to be quenched. Consequences of these results are examined.