In this paper, rheological parameters, in particular yield stress and consistency index, for viscoplastic fluids are inferred from elevation hydrographs derived from experiments. The direct model consisting of shallow water equations with a Herschel–Bulkley rheology is used to simulate a fluid flowing down an inclined plane and past a cylindrical occlusion. Numerical simulations are validated with experimental and related results from the literature. The aim is to infer the unknown rheological parameters using hydrograph measurements in the contact line region between the fluid and the occlusion. The rheological identification problem is formulated to minimize an objective functional that measures the discrepancy between the elevation hydrographs from the model output and experimental data. The inverse solver is tested on both synthetic and laboratory data. The set of rheological parameters inferred is compared with the values measured on a rheometer for the fluid used in the experiments. Inference of the unknown flow quantities from the wetting free-surface data has direct applications not only in industrial settings, to predict the wetting dynamics, but also in geophysical ones for risk assessments and management plans.