A single polystyrene sphere of radius a, between 141 and 275 micron, when in jected into a disk-plate (torsional) flow of polybutene (viscosity 36 poise, Mn ∼680), migrates radially inward at a rate that is dramatically increased by dissolving 1% of a high-molecular-weight polyisobutylene (Mv ∼106) to make the fluid viscoelastic. The torsional flow field was created by rotating a 21-cm-diameter disk at a rate ω of 6–9 rpm with a gap H of 3.7–5.4 mm between this and a ground glass plate with the fluid in the gap. Lateral migration toward a lower shear rate increased with increasing shear rate and with increasing shear rate gradient in the manner predicted by Brunn (1976) or Chan and Leal (1977). Shear rates up to 25 s−1 were investigated. Below a shear rate of 8 s−1 the radial migration velocity is of the form vr = − La/H)2r, where L is a positive constant containing the fluid properties, and r is the radial position of the particle.