  Based on the general form of the master equation for open quantum systems the
tunneling is considered. Using the path integral technique a simple closed form
expression for the tunneling rate through a parabolic barrier is obtained. The
tunneling in the open quantum systems strongly depends on the coupling with
environment. We found the cases when the dissipation prohibits tunneling
through the barrier but decreases the crossing of the barrier for the energies
above the barrier. As a particular application, the case of decay from the
metastable state is considered.
