This paper focuses on the study of momentum transfer rate between granular phases in particulate flows that interact in low and moderate volume fractions. Two systems have been created and simulated The first system included two granular phases initially mixed homogeneously in a vessel with rectangular cross section The second system included two granular phases as two concentric cylinders initially separated, but one phase was stationary and the other phase penetrated across a circular opening to the other phase In one hand, discrete element method (DEM) was employed as the particle trajectory following method, and on the other hand, an Eulerian approach was used as the continuum model to study the momentum transfer between granular phases The results ale also assessed based on the formula derived by Syamlal [Syamlal, M The Particle Particle Drag Term in a Multiparticle Model of Fluidization Topical Report, DOE/MC/21353-2373. NTIS/DE87006500, National Technical Information Service, Springfield, VA. 19871 for the solid solid momentum transfer rate This formula yields solid solid drag forces larger than those obtained from the DEM simulations especially as volume fraction grows Our results revealed that in the Eulerian model (in FLUENT) the relative velocity of granular phases during the interacting period may not be influenced only by the solid solid drag force Though the two approaches calculate qualitatively similar results in time, there are quantitative differences in calculation of phase volume fractions and the momentum of phases. The interacting phases are highly scattered in the Eulerian model predictions, which may be due to larger drag forces and a lower energy dissipation rate existing in the model.