Modern computational rheology techniques are used to interpret an experimental observation, which has remained unresolved for over four decades. The simple flow in question involved the rotation of a solid sphere in an infinite expanse of non-Newtonian elastic liquid. Under some conditions, Giesekus observed an interesting secondary flow. This added an ‘inertial’ secondary flow near the rotating sphere to the well-understood ‘slow-flow’ features observed and predicted by others in the 1960s. By employing a Phan-Thien/Tanner (PTT) constitutive model and moving away from the restriction of ‘slow-flow’, we show that it is possible to predict numerically the inertial vortex observed by Giesekus.