We describe a procedure for modelling the behaviour of multi-mode astronomical interferometers. The procedure is based on the concept of eigenfields. The input and output eigenfields are those field distributions on the sky and at the detector to which the individual telescopes of an interferometer can couple. The eigenfields of different telescopes are orthogonal, and therefore provide, when combined, a suitable basis set for propagating the second-order statistical properties of the field from a source through the telescopes, through the beam combiners, and onto the detectors. The scheme can be used at any wavelength, with any configuration of optical components (Michelson, Fizeau, etc.), with a source in any state of coherence and polarisation, and with any kind of detector.