In this study, an analytical model to resolve the water profiles equation of free surface flows through riprap has been developed. This model is based on Stephenson's relation to determine the head loss for different flow states in order to see its ability to reproduce the water profiles. This analytical model has been applied to experimental series realized in a rectangular channel built at the National Agronomic Institute of Tunisia (INAT) in collaboration with engineering consultants of the firm MECATER and in partnership with the INP Toulouse. MECATER is interested in these flows within the framework of a project with the nickel company SLN of ERAMET group in New Caledonia, concerning the protection of mining sterols against water flows at high mountains.