The present work applies the kinetic theory approach initiated by Reeks (1991; 1992) to model disperse phase stresses in multiphase flows. This approach offers an alternative to the standard derivation of the Eulerian continuum equations that has not yet found wide application in multiphase flow simulations. A comprehensive exposition of the theory in its simplest form is given eliminating errors and inaccuracies found in the literature, and then extended to a two-way coupled model taking into account the back-action of the disperse phase on the continuous one. An additional insight provided beyond standard Euler–Euler modeling is that the disperse phase pressure and stress derive from those of the liquid rather than being imposed by additional constitutive relations. Moreover, the availability of a simplified solution of the disperse phase kinetic stress equation allows to include the velocity fluctuations of the disperse phase, which have been neglected in many works based on standard Euler–Euler modeling. The resulting disperse phase stress model is implemented in the Open Field Operation and Manipulation (OpenFOAM) Foundation software and validated by comparison to a database of experimental results collected from the literature comprising a variety of configurations.