This work analyzes the flow of elongated particle suspensions through a converging-diverging channel. The model considers a suspension of rigid, elliptical particles dispersed in a Newtonian solvent liquid in which the viscous stress obeys Newton's law with a viscosity-like parameter that depends on both particle local concentration and particle axis aspect ratio. The phenomenon of shear-induced particle migration is described by the well-known Diffusive Flux Model with an additional diffusive flux related to the curvature of the streamlines. The average particle orientation in the flow is given by the principal direction of a particle conformation tensor. Both particle concentration and average particle alignment are used to define an additional anisotropic viscous stress in the suspension constitutive model. The resulting set of fully coupled, non-linear equations is solved by the DEVSS-TG/SUPG Finite Element Method. The results show the local particle concentration and average particle orientation in the flow domain, highlighting the behavior of the suspension microstructure near shear-dominated and extensional-dominated regions. (C) 2017 Elsevier B.V. All rights reserved.