The quality of consistent lumped-parameter models of rigid footings is examined. Emphasis is put on the maximum response during excitation and the geometrical damping related to free vibrations. The optimal order of a lumped-parameter model is determined for each degree of freedom, i.e. horizontal and vertical translations as well as torsion and rocking, and the necessity of coupling between horizontal sliding and rocking is discussed. Most of the analyses are carried out for hexagonal footings; but in order to generalise the conclusions to a broader variety of footings, comparisons are made with the response of circular and square foundations.