We report an innovative high pressure method combining the diamond anvil cell device with the technique of picosecond ultrasonics. Such an approach allows us to measure sound velocity and attenuation of solids and liquids under pressure of tens of GPa, overcoming all the drawbacks of traditional techniques. The power of this experimental technique is demonstrated in studies of lattice dynamics and relaxation processes in a metallic single grain of AlPdMn quasicrystal, and in rare gas solids neon and argon.