Picosecond ultrasonics is used to study the damage or degradation of Mo/Si multilayers caused by laser irradiation. Changes of surface phonon spectra in multilayers due to femtosecond laser damaging are observed in a regime of extremely low fluence level, well before the onset of melting, delamination, distortion, or material interdiffusion. It is found that the damage is shallow in depth (top few layers), and its mechanism is laser-induced changes in acoustic impedances, most likely due to stress relaxation. Its effects on extreme ultraviolet (EUV) reflectance and implications for projection EUV lithography are also discussed. We believe this technique has a potential application as a highly sensitive tool capable of detecting low-degree or early-stage damage of multilayers.