Consideration is given to the effect of viscoelasticity on the flow of non‐Newtonian liquids past a cylinder contained in a confined geometry. Both flow visualization and force measurements are discussed. It is shown that the proximity of a bounding wall near the cylinder results in a force on the cylinder at right angles to the mean flow direction and toward the wall. Over the range of flow conditions available, the total drag on the cylinder is reduced by the presence of viscoelasticity. This conclusion is shown to be true for ‘constant‐viscosity’ elastic liquids and also for those that exhibit substantial ‘shear thinning.’ To facilitate this, experiments are carried out on Newtonian liquids, Boger liquids, aqueous solutions of polyacrylamide, and aqueous solutions of Xanthan gum. Attempts to simulate numerically the flow in the cylinder problem using modern finite‐element techniques are shown to lead to qualitative agreement with the experimental observations.