By specializing the class of unsteady extensional flows considered by Slattery to motions which are periodic perturbations about a rest state and using the proper representation for Noll’s simple fluid undergoing such flows, explicit formulas for the induced stresses in terms of measurable material properties were achieved. It is found that oscillations of a sufficiently large amplitude will generate steady stresses in the fluid due to its nonlinear viscoelastic properties implying that orientation effects might be found in such flows.