This investigation concerns a prediction of the behavior of viscoelastic fluids in a parallel circular squeeze film with a constant approach velocity, and a comparison to experimental results. The squeeze film geometry has direct application to unsteady hydrodynamic lubrication. The analysis predicts that load capacity of a viscoelastic fluid may be increased due to normal stress effects or decreased due to a delayed response of shear stress to a change in shear rate. Ten tested fluids include Newtonian control fluids, silicone fluids, high molecular weight polymers in petroleum oils, and extremely high molecular weight polymers in water and glycerin. The experimental squeezing is accomplished by the free fall of a cylindrical steel rod along its axis toward a stationary opposing surface. Film thickness, velocity of approach and load are measured. The velocity of approach is essentially constant in the range of film thickness considered. The water-glycerin-polymer solutions exhibited load capacity increases up to 33 percent, while the petroleum-polymer and silicone fluids showed decreases to 23 percent. It appears that viscoelastic effects cannot account for the reported improved bearing performance of polymer-additive lubricants.