The behavior of rigid and deformable particles suspended in viscoelastic fluids undergoing slow Couette and Poiseuille flows was studied experimentally. In tube flow, the particles migrated from the wall to a limiting radial position at which the velocity gradient was effectively zero; in Couette flow between concentric rotating cylinders, migration occurred towards the outer cylinder wall. The rotations of rigid rods and disks were similar to those in Newtonian liquids, except for a steady drift in orbit constant to asymptotic values which in Newtonian liquids correspond to minimum energy dissipation. Two‐body collisions of rigid uniform spheres were unsymmetrical and irreversible. The deformation and burst of Newtonian liquid drops were as in Newtonian suspending liquids of comparable suspending phase viscosity, except for the alignment angle of the drop at zero deformation.