An analysis is presented to find the effect of the elasticity of the lubricant in polymer containing multigrade oils on the performance of a dynamically loaded rotor, supported by short journal bearings. This paper solves for the loci of the center of a journal, subjected to unsteady loading, using Newtonian and viscoelastic lubricants. The viscoelastic fluid is described by a relatively new rheological equation which has been shown to be successful in predicting the experimental trends of various unsteady high shear rate flows. The analysis is a perturbation solution for low Deborah numbers where the stress relaxation process is a first-order effect. The results show an improvement in the performance of viscoelastic lubricants over Newtonian lubricants. Under an unsteady load, the journal center orbits show reduced eccentricity and travel of the journal due to the elasticity of the fluid. It implies that lubricants with a longer relaxation time can be developed where the viscosity and viscous losses can be reduced without adverse effect on the wear, resulting in a significant saving of energy.Presented as a Society of Tribologists and Lubrication Engineers paper at the ASME/STLE Tribology Conference in Toronto, Ontario, Canada, October 8–10, 1990