Abstract <p>A computational algorithm for calculating flows of nonequilibrium gas-dispersed media (gas–solid particles, gas–liquid droplets) with a low volume concentration of the dispersed phase has been developed. Within the Euler–Euler approach, a fully continuous description of the two-phase medium is implemented based on the mathematical model for two-phase flows by A. Chinnayya, R.&#xa0;Saurel, and Q. Carmouze (2016). The effect of pressure and phase velocity relaxation is taken into account during phase interaction. The computational algorithm utilizes the high-resolution Godunov method and HLL Riemann solver. The main focus is on accounting for the influence of phase velocity nonequilibrium (slip) on the relationship between the trajectories of particles and the gas phase, as well as on the interaction of the dispersed phase with solid walls. Test calculations are carried out in the case of a one-dimensional flow of a two-phase medium and methodological studies examining how the particle size and the dispersed-phase volume fraction affect the structure and parameters of gas-dispersed flows in two-dimensional regions bounded by solid surfaces.</p>