The effect of screening by atomic electrons on the scattering of relativistic electrons by heavy atoms has been computed numerically using different screening models. Exponential and Hartree potentials were used to simulate the screening. The asymmetry factor S(θ) and the differential scattering cross section d σ(θ) dΩ were computed at 15 degree intervals from 15° to 165°. We report here the results for (a) 121 keV electrons scattered by gold, Z = 79, using two exponential potentials of different range, (b) 79 keV (v/c = 0.5) electrons scattered by mercury, Z = 80, using exponential and Hartree fields, (c) 46 keV ( v c = 0.4) electrons scattered by mercury as in (b). The asymmetry factor S(θ) and dσ dΩ(θ) were computed using a partial wave expansion in which the phase shifts were obtained both by numerical integration of a suitably transformed Dirac radial equation and also computed in WKB approximation. The results are compared with corresponding calculations for the Coulomb field. In general the differences are no more than a few percent, but below 30° the screened field cross-sections are as much as 50% smaller.