The eddy interaction model (EIM) is in common use in simulations of turbulent particulate flow. In the model, particle motions are determined by interactions with random-velocity fluid eddies. Spatial and temporal velocity autocorrelations land therefore wave number and frequency spectral are characterised by the probability distributions of the velocity, length and time scales of the eddies. In this paper, spectral behaviour of both standard and modified EIMs is examined. The whole range of behaviours of the EIM, characterised by polynomial velocity autocorrelation functions, is studied. It is shown that each of the resulting spectra exhibits unphysical characteristics. Consequences for modelling are discussed briefly.