Micromechanical models for the instantaneous elastic stress tensor tau of "film fluids," i.e., fluids with internal interfaces such as foams, emulsions, and immiscible blends, yield formulas that are similar to each other and are well approximated simply by tau proportional to C-1/2, where C is the Cauchy strain tenser. This expression can be derived as an approximation by assuming that the interfaces deform affinely and that the tension in the interface is independent of the deformation. The expression tau proportional to C-1/2 is, therefore, the analog of the classical expression tau proportional to C-1 for the instantaneous elastic stress in polymeric "line fluids." The second normal stress difference of a "film fluid" is predicted to be negative and of comparable magnitude to the first normal stress difference.