Abstract: In recent years, the first-order finite-volume Osher scheme has been applied with success to a dozen model problems and practical cases involving two-dimensional shallow-water open flows. This paper discusses for the first time relevant techniques in its algorithmic implementation. A kernel lies in the setup of a cell hydraulic model-step flow, which can be described mathematically by a special type of Riemann problem. It can be solved approximately by reducing to a standard Riemann problem in gas dynmaics, and correcting the results accordingly. Based on theoretical analysis and numerical tests, a detailed description is also given about various types of outer, inner and moving boundary treatments, so that a complete and practical algorithm has been formed.