The surface acoustic waves (SAWs) technique is becoming an attractive tool for accurately and nondestructively characterizing the mechanical property of the fragile low dielectric constant (low-k) thin film used in the advanced ULSI multi-layer interconnects. The dispersion features of SAWs propagating on the layered structure of low-k/SiO2/Si substrate and low-k/Cu/Si substrate are investigated in detail. The influence of the film thickness on the dispersion curvature is provided as an instruction for an accurate and facile fitting process. Numerical results indicate that the mechanical property of low-k films is expected to determine effectively when the broadband frequency is up to 300 MHz.