The propagation characteristics of interface waves are studied theoretically and experimentally. The problem of solving for roots of characterization equation of interface waves are discussed. It is shown that all roots can be found by means of Riemann sheet analysis. The propagation mechanism of Stoneley wave, Leaky Rayleigh and Leaky interface waves are explored, the wave vector and displacement behaviors of these waves are illustrated to show their differences. At last, the interface waves are measured with laser ultrasonic technique based on photo-elastic effect, and the experimental results are in good agreement with theoretical predictions.