  We study the phenomenon of macroscopic quantum tunneling (MQT) in small
Josephson junctions (JJ) with an externally applied magnetic field. The latter
results in the appearance of the Fraunhofer type modulation of the current
density along the barrier. The problem of MQT for a point-like JJ is reduced to
the motion of the quantum particle in the washboard potential. In the case of a
finite size JJ under consideration, this problem corresponds to a MQT in
potential which itself, besides the phase, depends on space variables. Finally,
the general expression for the crossover temperature T_0 between thermally
activated and macroscopic quantum tunneling regimes and the escaping time
tau_esc have been calculated.
