Poiseuille flow of an elastico-viscous liquid in a straight, circular pipe driven by a pressure gradient oscillating about a non-zero mean is investigated. The simple fluid of the multiple integral type presents a flow enhancement which depends on the frequency and amplitude of the oscillation, magnitude of the mean pressure gradient and the material functions of the fluid. A closed form expression for the flow rate alteration, independent of any explicit representations for the material functions, is developed at the lowest order in the perturbation algorithm where nonlinear effects appear. Asymptotic analyses of the flow rate enhancement at small and large frequencies are presented. © 1991.