The paper describes a new time-marching method for calculating two-dimensional, dilute, nonturbulent, gas-particle flows using an Eulerian formulation. The method is accurate and robust, and overcomes many of the deficiencies of other schemes reported in the literature. A particular feature is the ability to calculate the particle density field accurately even in the vicinity of discontinuities, particle-free 'shadow' zones and particle separations from solid surfaces. The paper discusses the ill-posedness of the Eulerian equations and describes the numerical scheme, focusing on (i) the particle boundary condition at solid surfaces, (ii) the capture of discontinuities in the particle density field, (iii) special techniques to handle shadow zones, (iv) convergence acceleration for particle flows with very small Stokes numbers and, (v) the possibility of crossing particle trajectories. Applications of the method are illustrated by calculations of particle flow over a circular cylinder and through a turbine cascade. The results agree well with the predictions of a computationally more expensive Lagrangian tracking code and the method offers the possibility of extension to include turbulent particle transport. (C) 2000 Elsevier Science Ltd. All rights reserved.