Start-up times in viscoelastic channel and pipe flows generated by the sudden imposition of a pressure gradient are here determined by a mixed analytical/numerical procedure. The rheological models considered are the upper convected Maxwell and the Oldroyd-B equations. With these models the flow evolves asymptotically to the steady state solution after a transient regime presenting strong oscillations of the velocity fields, hence implying a special procedure for the calculation of the start-up time. This time interval required for establishment of steady flow tends to increase significantly with elasticity, at a constant rate of increase for the UCM model, but the increase becoming less than linear for the Oldroyd-B model. No wiggles or artificial oscillations were observed for the variation of the start-up times with the elasticity number.