Finite Volume two-dimensional shock-capturing model. The numerical model solves the two-dimensional shallow water equations with different modes of sediment transport (bed-load and suspended load) (Canestrelli et al. 2009, Canestrelli et al, 2010). The scheme solves the system of partial differential equations cast in a non-conservative form, but it has the important characteristic of reducing automatically to a conservative scheme if the underlying system of equations is a conservation law. The scheme thus belongs to the so-called category of “shock-capturing” schemes. At the present I am adding a new module for the computation of mud flows, and I want to apply the model to the Fly River (Papua New Guinea) system.