At low temperatures and for moderate surface charge densities, electrons in inversion layers on (100) $p$-type Si are two-dimensional in character; i.e., they occupy only one electric quantum level, or sub-band. For electron densities greater than about 6 \ifmmode\times\else\texttimes\fi{} ${10}^{12}$ per ${\mathrm{cm}}^{2}$, depending upon substrate doping, we have observed deviations from two-dimensional behavior in oscillatory magnetoconductance (Shubnikov-de Haas) measurements, which are interpreted as evidence of the onset of occupation of a higher sub-band. The effects of such occupation of higher sub-bands have been calculated for the four different resistivities used in the experiments. The observed change in effective density of states [(10-20)%] and its dependence upon substrate resistivity are in good agreement with theory. The experimental values for the threshold charge densities for higher sub-band occupation are higher than the theoretical values by a factor of about 1.5.