A self-consistent-field approximation has been applied to the continuous-representation version of statistical theory. Calculations have been carried out for He(3S and 1S), Be2+(1S), Be(1S), and Ne(1S). Binding energies are about 6% greater than experimental values. No shell structure in electron density was obtained, however, which reflects an inadequacy of the theory in approximating such properties. Nevertheless, the densities obtained gave relatively good estimates of the mean values of rn, −2≤n≤+2.