In this symposium paper, the migration and hydrodynamic diffusion of non-colloidal, spherical particles suspended in polymer solutions are considered under Poiseuille or torsional flows. The migration phenomena in polymer solutions are compared with those in Newtonian fluids and the effect of fluid elasticity is discussed. The experimental results on particle migration in dilute polymer solution reveal that even a slight change in the rheological property of the dispersing medium can induce drastic differences in flow behavior and migration of particles, especially in dilute and semi-concentrated suspensions.