Consideration is given to the suppression of the radial and polar escape of magnetic flux in the form of toroidal flux tubes (flux rings) from low latitudes in the overshoot region below the solar convection zone through the combined action of the subadiabatic ambient stratification and the rotationally induced forces. It is shown that a flux ring which is initially in thermal equilibrium with its environment and rotates with the ambient angular velocity moves radially and latitudinally towards an equilibrium configuration of lower internal temperature and larger internal rotation rate with respect to the surrounding nonmagnetic gas. Flux rings perform superposed buoyancy and inertial oscillations around their equilibrium positions. From a study of the frequencies and amplitudes of these oscillations, it is concluded that flux rings with B of less than about 100,000 G can be kept within the overshoot region if the superadiabaticity is sufficiently negative, i.e., less than about -0.00004.