Thin film drainage measurements are presented for submicron films of an "ideal elastic" or Boger fluid, which is a high molecular weight polymer solution in a high viscosity solvent. The measurements are made in a surface force apparatus, with the fluid being squeezed between two mica surfaces in a crossed cylinder geometry and the film thickness measured as a function of time to study its drainage behavior. No equilibrium surface forces are detected in this system, indicating that the polymer is nonadsorbing. The effect of fluid elasticity is predicted to make drainage more rapid in a Boger fluid than for the equivalent Newtonian fluid. Qualitatively this is what is observed for films less than 600 nm thick, but the drainage is even more rapid than predicted for the elastic fluid. To account for this, it is suggested that slippage is occurring at the fluid-solid interfaces, and the data is analyzed in terms of a simple slip model. The slip length required to fit the data is in the range 30-50 nm. (C) 2000 American Institute of Physics. [S0021-9606(00)71413-9].