By use of simplified multiple collision model we calculate the inclusive differential cross section for antikaons produced in relativistic nucleus collisions at bombarding energies per nucleon below the threshold for production from free nucleon nucleon encounters. The primordial spectrum obtained is in qualitative agreement with experimental data for the reaction Si + Si at 2.1 GeV/nucleon. The inclusion of the rescattering and absorption of the antikaons significantly influences the shape of the primordial spectrum but does not substantially alter the degree of agreement with the experimental data.