This paper summarizes the results from an experimental investigation of the effects of eccentricity and rotational speed on the free surface shape on a viscoelastic liquid between eccentric cylinders. In the experimental geometry, the inner cylinder rotates and the outer cylinder is stationary. The experiments show that there is a circumferential pressure gradient (the lubrication effect) which has a dominant influence on the free surface shape at all eccentricities and rotational speeds. For a liquid with small normal stress effects, the normal-stress induced component of the deformation tends to be overwhelmed by the lubrication effect, whereas a liguid with large normal stress effects exhibits characteristics normal-stress induced deformations at small eccentricities and rotational speeds. There is good agreement between experiment and second order predictions for the large normal stress liquid under these conditions. The ranges of eccentricities and rotational speeds for which second order theory describes the low normal stress liquid appear to be much more limited and are difficult to reproduce experimentally. © 1984.