Exact solution is derived for axisymmetric flow during water injection with fine particles detachment, migration, attachment and straining. The solution contains the so-called erosion front described as a weak discontinuity, behind which the mechanical equilibrium of attached particles holds and the dynamic attachment occurs ahead of the front. Introduction of a timely potential form for suspended concentration decreases the order of governing system allowing derivation of the erosion front trajectory. The analytical model describes the injectivity decline due to fines migration and reveals non-monotonic injection rate dependency of the well index.