A Lagrangian finite element method is used to simulate the transient sedimentation of spheres in polymeric liquids. The liquid is described by an integral constitutive equation of the Rivlin-Sawyers type. The simulations show a marked increase in the drag, which is apparently related to the elongational flow in the wake. Furthermore, the results indicate that the sedimenting sphere geometry is a possible candidate for a rheometer capable of providing information about fluids in extensional flows.