This paper presents two advanced acoustic methods for the determination of anisotropic elastic constants of deposited thin films. They are resonant-ultrasound spectroscopy with laser-Doppler interferometry (RUS/Laser method) and picosecond-laser ultrasound method. Deposited thin films usually exhibit elastic anisotropy between the film-growth direction and an in-plane direction, and they show five independent elastic constants denoted by C11,C33,C44,C66 and C13 when the x3 axis is set along the film-thickness direction. The former method determines four moduli except C44, the out-of-plane shear modulus, through free-vibration resonance frequencies of the film/substrate specimen. This method is applicable to thin films thicker than about 200 nm. The latter determines C33, the out-of-plane modulus, accurately bymeasuring the round-trip time of the longitudinal wave traveling along the film-thickness direction. This method is applicable to thin films thicker than about 20 nm. Thus, combination of these two methods allows us to discuss the elastic anisotropy of thin films. The results for Co/Pt superlattice thin film and copper thin film are presented.