The research on the transport of fine particles in saturated porous media under elastic waves is complementary to the current study of particle migration in static multi-phases or steady-state seepage flow. Considering the influence of elastic waves on particle detachment-migration-capture process, we established a modified model of fine particle transport under elastic waves, and analyzed the changes of particle migration and physical properties in reservoir. Furthermore, the critical velocity of particle detachment from the pore surface under elastic waves was derived, which was found negatively related to the fluid viscosity and particle/pore-throat radius ratio, but positively related to the degree of matrix cementation, structural force, particle radius and density. It also shows the smaller the particle/pore-throat radius ratio is, the stronger the impact of wave imposing on particle detachments is. The model also considers the changes of flow rate under waves. When the detachment rate of fine particles increases, the retention rate of deposition would increase firstly and then decline with wave attenuation and time extension, and the retention rate of throat-blocking would rise. It demonstrates that the elastic wave not only leads to an enhancement in the capacity of particle detachment and suspension, but increases the possibilities of "bridge" blocking in micro throats. This study might be useful to the exploration on rock physical properties in petrophysics and industrial wave application.