summary. A new technique is presented for modelling the elastic constants of cracked structures with application to systems with weak concentrations of parallel cracks, and of simple biplanar and triplanar cracks. The velocities and Vp/Vs ratios of these anisotropic structures are used to provide quantitative models for some earthquake precursors. These results indicate the great importance of crack geometry to the behaviour of precursors. The velocities of saturated cracks appear to favour the dilatancy-diffusion model of precursory phenomena. Synthetic seismograms are calculated for propagation through possible dilatancy zones. The seismograms show some characteristic features which may be useful for the investigation of earthquake dilatancy.