The influence of the shape and elastic-strain fields of buried quantum dots (QDs) on the angular distribution of diffuse X-ray scattering is studied. Elastic lattice displacements were calculated using the Green function method. Diffuse scattering from a semiconductor matrix with QDs having the shape of a cylinder, truncated cone, and spheroid was numerically simulated. It is shown that angular distributions of diffuse scattering for QDs with different shapes have significant distinctions at a small volume density of nanostructures in the crystal. At a large QD density, which is typical for superlattices, these distinctions become weak.