Hydrodynamic interactions between the component bodies of a multi-body offshore system can cause substantial enhancement of certain load effects, such as mean horizontal drift forces and radiation damping. It is found, for example, that for a group of N similar members these forces can be of the order of N2 times the force on one member in isolation, over a range of low frequencies; and at higher frequencies interaction effects continue to have important consequences on design parameters. This paper discusses some theoretical background which sheds light on this phenomenon, and presents numerical results for semisubmersible, TLP and other configurations which provide further insight. The numerical evaluation of wave flow past these complex multibody systems is performed using a coupled finite element/boundary element model, together with the near field (direct integration) calculation of drift forces. Results are compared with an existing approximate method, and with idealizations based on the columns alone, with a view to the development of simple procedures for hydrodynamic synthesis.