Radioactivity induced in detectors by protons and secondary neutrons is the major background source of gamma-ray telescopes. A significant background reduction will be achieved by the use of an anticoincidence shield surrounding the Ge detector of the INTEGRAL spectrometer (SPI). An important aspect in the design of SPI was therefore to find the optimum thickness of the shield. In general, the hadronic interactions triggered by energetic cosmic rays in the detector are very difficult to simulate with good accuracy. Now, however, the TIERCE code developed at CEA/DAM Bruyeres-le-Chatel enables us to make these computations with a good accuracy. It is indeed a Monte Carlo code which transports hadrons, neutrons, electrons and gamma, based upon cross sections measurements obtained in accelerators in parallel with the program conception. In that sense, it is one of the only code able to simulate correctly the spallation reactions. We have then used this code to evaluate the neutron production induced in the SPI anticoincidence shield by the cosmic GeV protons, and to deduce information about the positron and neutron fluence, the activation products in Ge for different BGO shield thickness and to determine the impacts of the shield on the induced background.