Nondestructive evaluation of elastic properties of advanced materials was performed with short surface acoustic wave (SAW) pulses in the 10 MHz-300 MHz range. The elastic surface pulses were launched thermoelastically with pulsed laser radiation and detected with a piezoelectric foil transducer. This technique was used, for example, to determine the mechanical and elastic properties of superhard materials, such as microcrystalline CVD diamond films and submicrometer thick nanocrystalline films of cubic boron nitride. These results are compared with the properties of the corresponding single-crystal material, In layered systems or graded materials the introduction of a length scale leads to dispersion of the surface acoustic waves (SAWs), which allows the simultaneous determination of several properties, such as the density, Young's modulus, and Poisson ratio. In free-standing polycrystalline CVD diamond plates dispersion of elastic surface pulses was observed. This material is neither isotropic nor homogeneous because the grain size and structure vary from nucleation side to the growth side. In some samples anomalous dispersion of SAWs was observed on the nucleation side with the finer grains. Amorphous SiCxNy films with various compositions were investigated to compare the microscopic bonding characteristics, determined by molecular dynamics (MD) simulations, with the macroscopic mechanical properties obtained by surface acoustic wave spectroscopy (SAWS).