We report measurements for the effects of hydrostatic pressure on several cross-sectional areas for the electron and for the hole sheets of the Fermi surface of Cd. Pressure derivatives were obtained at a temperature of 0.4 K using a fluid-He phase-shift technique in which the data are digitally recorded and analyzed. Calculations based on a semiempirical nonlocal pseudopotential band structure due to Stark are compared with the experimental results. The anisotropy observed in the pressure dependence of the electron sheet confirms the negative sign of the [0002] pseudopotential in this model. The pressure derivative of largest magnitude is for the [11\ifmmode\bar\else\textasciimacron\fi{}20] cross section of the cap and is given by $\frac{d(\mathrm{ln}S)}{\mathrm{dp}}=\ensuremath{-}(13.0\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ ${\mathrm{kbar}}^{\ensuremath{-}1}$.