We have developed laser-ultrasonic methods to evaluate the elastic properties of thin films. Our method, called SAW spectrometry, used broadband surface acoustic waves (SAWS) generated by a line-focused, pulsed laser. SAWS with frequency components up to similar to 400 MHz were detected by a Michelson interferometer. Dispersion relations for the phase velocity vs. frequency were calculated from displacement waveforms acquired over a range of source-detector separations. Quantitative elastic-property information was obtained from the dispersion relations with a newly developed inversion algorithm. The algorithm was based on the delta-function representation of the elastodynamic Green's function for anisotropic layered systems. The methods were tested by applying them to a molybdenum film on a single-crystal silicon wafer. Values obtained for the film's Poisson ratio and Young's modulus were consistent with literature values. We also used SAW spectrometry to investigate several samples containing titanium nitride films on silicon substrates. Assuming literature values for the filet density and Poisson ratio, we applied the inversion algorithm to determine the thickness and Young's modulus of each film, Young's modulus in the films was found to increase monotonically with increasing film thickness from 368 to 453 GPa. Inversion results for the film thickness were in very good agreement with destructive measurements of the actual thicknesses.