Solutions to the equation of motion have been obtained for a viscoelastic fluid which obeys an Oldroyd three‐constant constitutive equation. The solutions apply to a fluid at rest which at zero time is subjected to (1) a step change in pressure gradient or (2) a sinusoidally varying pressure gradient. From these results one can predict the response of the fluid to an arbitrary time‐dependent pressure gradient. Curves are presented which show how the flow of a viscoelastic fluid, when subjected to a step change in pressure, can overshoot the final steady‐state flow. Amplitude and phase relationships between different variables are presented for a sinusoidally varying pressure gradient. Comparisons are made with available experimental data.