The study of the storage of toroidal flux tubes at the base of the convection zone is of interest in connection with the operation of a solar αΩ-type dynamo. The natural equilibrium state for an isolated flux tube is that of neutral buoyancy (so that there is a mass flow along the tube in the direction of solar rotation); flux tubes in thermal equilibrium must be ruled out for magnetic fluxes Φ ≳ 1019 Mx. In this paper we study the equilibrium and stability properties of toroidal flux tubes in the equatorial plane of the Sun. To that end, we use a solar model which includes a consistently calculated overshoot region at the bottom of the convection zone, based on a nonlocal mixing length formalism. As a consequence of the nonlocal treatment, the superadiabaticity already becomes negative in the lowest part (≃26,000 km) of the convection zone proper, which is defined as the region in which the convective flux, is positive. In the present model, the underlying overshoot region extends over some 10,000 km, and the total extent of the subadiabatic layer is about 36,000 km. For the angular velocity distribution, we use a semiempirical formula based on helioseismological results. Flux tubes with field strengths of about 105 G can be stored only in the overshoot region, while tubes with equipartition field strength could be kept in a subadiabatic layer at the bottom of the convection zone proper. The results of the stability analysis are compared with those of previous studies.