Fines migration involving particle detachment in reservoirs often leads to severe permeability damage. It is the consequence of straining of the detached fines in relatively narrower pore throats. Many laboratory coreflood tests indicate that the time of permeability stabilisation can reach hundreds or thousands of pore volumes injected. However, the classical filtration theory assumes that the mobilised fines are transported by the bulk of the carrier fluid, thus the permeability stabilises after one pore volume injected. The current paper attributes the stabilisation delay to the slow drift of the released fines close to the rock surface. We propose the system of flow equations for fines migration in porous media taking into account the velocity of particles lower than that of the fluid. An analytical model for one-dimensional flow with particle mobilisation and straining during piecewise increasing flow rate is obtained. The laboratory data are in good agreement with the results of mathematical modelling. The effective particle speed is 500-1000 times lower than the water velocity.