Separation of particles from the carrier fluid of suspension is important in many engineering applications. In this work numerical simulations of particle migration during the flow of concentrated suspension through 3D asymmetric T-shaped bifurcating channels were carried out. The carrier fluids were considered to be non-Newtonian and inelastic. Diffusive flux model of shear-induced migration in conjugation with the power-law and Bird-Carreau constitutive models for the carrier fluid was used in the simulations. The velocity and particle concentration profiles in a non-Newtonian suspending fluid showed marked differences compared to that in the Newtonian carrier. Enhanced migration was observed in the case of shear thinning fluid while low for shear thickening. The symmetric velocity and concentration profiles in the inlet branch become asymmetric in the daughter branches and the degree of asymmetry strongly depends on the carrier fluid rheology. The results showed that the particle partitioning between daughter branches do not follow the fluid partitioning and the degree of separation depends on the relative volumetric flow rate of bulk suspension in the daughter branches. Higher separation efficiency was achieved for suspension in shear thinning fluid and relatively lower in Newtonian and shear thickening fluids.