Double strangeness production, i.e. the net production of two s quarks and two overlines quarks (carried inside hadrons) in antiproton-nucleus annihilations is investigated theoretically. The various mechanisms are identified, both for conventional B = 0 and for unusual B = 1,2 annihilations. The double strangeness yield is estimated. The lack of precise input data for some reactions is underlined. The results are compared with the recent data of the DIANA collaboration. They seem to be consistent with the conventional processes.