Based on mesoscopic heterogeneity theory model of Pride and Berryman, coupled dynamical equations were deduced with a group of displacements, and a group with displacement and pore pressure. With double-porosity model, elastic wave expression of phase velocity and inverse quality factor are deduced. Influence of mesoscopic flow on propagation of elastic waves was discussed. Numerical examples show that velocity of fast wave increases rapidly with increase of frequency, and mesoscopic flow loss is at least higher one order of magnitude than Biot loss. Besides, mesoscopic flow has different influence on slow wave. It is proved that mesoscopic flow is the main factor of wave energy loss and velocity dispersion.