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 D0 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 D0 detectors.
It is shown that a steel mask placed upstream of the detectors can reduce
the background rates by almost an order of magnitude.