From molecular dynamics simulations of liquid-liquid and liquid-vapor interfaces at low temperatures between two simple liquids we determine the Baus elastic constants [M. Baus, J. Chem. Phys. 74, 2003 (1981)] and their variation across the interface. For certain cases the nonlocal stress-stress correlation functions were also calculated. A two-phase system with a planar interface is characterized by five independent elastic moduli. Two moduli show a dramatic decrease inside the liquid-liquid interface, similar to the drop in viscosity ("lubricating effect") we found in sheared interfaces [P. Padilla, S. Toxvaerd, and J. Stecki, J. Chem. Phys. 103, 716 (1995)]. The other three, which are zero in the bulk region, show a oscillatory variation across the interface. One of these three is related to the surface tension.