Earlier low‐frequency results for scattering and reflection by random distributions of relatively arbitrary bosses on rigid or free base planes are applied numerically to completely rigid or free ellipsoidally embossed isotropic and anisotropic surfaces. Illustrative curves exhibit the effects of boss shape and orientation, and of their statistical distribution (pair correlated as well as uncorrelated) on the coherent power reflection coefficient and the reflected phase, and on the incoherent differential scattering cross section per unit area versus angles. In addition, for rigid surfaces, simple approximations are included for the location and magnitude of the pseudo‐Brewster minimum in the reflected power and for the extrema of the forward (specular) and backscattered cross sections, as well as for the location of the zero of the phase change on reflection. We emphasize anisotropic forward and backscattered differential cross sections near grazing for applications to sea–air, sea–bottom, and sea–ice programs.