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Detailed simulations were performed on beam loss rates in the vicinity of the Tevatron Collider detectors due to beam-gas nuclear elastic interactions. It turns out that this component can drive the accelerator-related background rates in the CDF and DO detectors, exceeding those due to outscattering from collimation system, inelastic beam-gas interactions and other processes. Results of realistic simulations with the STRUCT and MARS codes are presented for the interaction region components and the CDF and DO detectors. It is shown that a steel mask placed upstream of the detectors can reduce the background rates by almost an order of magnitude.