This article outlines a computational procedure for the prediction of dispersed two-phase, solid-liquid and gas-liquid, turbulent flows in baffled, impeller-stirred vessels common in the chemical industries. A two-flow Eulerian model is employed, based on the main assumption of interpenetrating coexisting continua. Mean momentum and mass conservation equations are solved for each phase and turbulent closure is effected by extending the single phase k-[epsilon] turbulence model to two-phase flows. The resulting set of highly coupled equations is solved by a two-phase implicit algorithm, PISO-2P, which allows calculation for a wide range of phase fraction, particle size and phase density ratios. Predictions are presented for solid-liquid and gas-liquid (bubbly) flows. Comparisons are made with experimental data for the mean phase velocities and volume fraction, mean slip velocity and turbulence quantities.