Simple analytical solutions exist for the deflection by line loads of thin elastic beams that overlie an inviscid fluid substrate. Deflections for more complex rectangular- and triangular-shaped loads can be evaluated by integration. The deflection of a beam that varies in thickness along its length is best solved, however, by numerical rather than analytical methods. Foremost among them are finite difference techniques, and both two- and three-dimensional codes are now widely available. Thin-plate theory and a flat Earth are good approximations to make in most geological modelling applications.