In this paper, we present the study of Raman Scattering by Surface Polaritons (SPs). Based on the Attenuated Total Reflection method (ATR method) and Raman Scattering method and refered to the method of Raman Scattering under ATRf conditions (RSATR) in Kretchmann configuration, we have suggested a method o RSATR with Otto configuration and have made a series of experiments on the sample of single crystal CaF2. Theoretically we have got a phenomenologioal dispersion relation of SPs on the boundary between CaF2 and air using the law of energy conservation and the law of momentum, conservation parallel the sample stirfaoe as well as general dispersion relation of SPs derived from surface Green fnnotion or surface response ftmotion. With the help of sample carrier specially designed, the experiment was carried out to measurle ihe dispersion relation of SPs. Comparison indicates that the experimental resnlis are in good agreement with that of theory.