Computations of gas-solid two-phase flow are carried out within the framework of mixture formulations. These computations are based on the Riemann problem for the resulting theoretical equations. The Riemann problem for the model equations is solved numerically using Godunov methods of centred-type. Numerical results are shown for carefully chosen test problems. The results show that both the model and the numerical methods provide very satisfactory solutions. © 2012 American Institute of Physics.