Detailed STRUCT simulations are performed on beam loss rates in the vicinity of the BTeV detector in the Tevatron CO interaction region due to beam-gas nuclear elastic interactions and out-scattering from the collimation system. Corresponding showers induced in the machine components and background rates in BTeV are modeled with the MARS14 code. It is shown that the combination of a steel collimator and concrete shielding wall located in front of the detector can reduce the accelerator-related background rates in the detector by an order of magnitude