In this paper we report on a computational study for the plane Poiseuille flow of a dense non-colloidal suspension at low Reynolds numbers. Our study is based on a recently developed two-phase model that appropriately accommodates constitutive relations for the suspension rheology and a migration model in the form of an advection-diffusion equation for the volume fraction of the granular phase [1]. Our numerical predictions accord well to experimental data and to previously reported numerical results based on a particle resolved method, especially as regards the particle distribution in the bulk of the channel. Further, we delineate the impact of the nonlocal stresses due to particle interactions on the structure of the flow and assess their effect on particle migration. Finally, we examine the role of these stresses in suspensions close to the jamming transition. (C) 2017 Elsevier B.V. All rights reserved.