SUMMARYIn this paper, several numerical schemes are extended to obtain approximate solutions to the system of equations encountered in the analysis of multiphase mixtures of gas and particles. Both dense and dilute mixtures are studied, the gas is modelled as a perfect gas and the solid is considered incompressible. Although the tests employed throughout this work for studying the behaviour of the schemes are essentially one dimensional, the finite volume method developed permits its application to multidimensional problems in unstructured grids.