Density scanning by gamma transmission measurements on whole cores is here demonstrated to be valuable both as a sampling guide in the core laboratory, and for assessing the degree of induration of Palaeogene limestones in Denmark. Fracture intensity is also indicated. Moduli of elasticity calculated from acoustic velocities are systematically related to density (and thus porosity), so we have attempted to relate the degree of induration to the dynamic moduli of elasticity. The dynamic moduli of elasticity fall, as is commonly observed, above those measured from uniaxial compression tests. P-wave as well as S-wave velocities are anisotropic in the entire porosity interval (12%–44%). This is reflected in a significant anisotropy of the dynamic shear modulus at high densities, whereas the anisotropy for lower densities and for the dynamic Young's modulus and dynamic bulk modulus remain below the level of significance. The anisotropy probably reflects minor horizontal fractures formed during exhumation of the limestone and unloading of the cores. The density scanning tool thus proves a useful method for determination of geophysical and geotechnical parameters.