In this paper, we study the existence and uniqueness of interfacial waves in account of surface elasticity at the interface. A sufficient condition for the existence and uniqueness of a subsonic interfacial wave between two elastic half spaces is obtained for general anisotropic materials. Further, we explicitly calculate the dispersion relations of interfacial waves for interfaces between two solids and solid and fluid, and parametrically study the effects of surface elasticity on the dispersion relations. We observe that the dispersion relations of interfacial waves are nonlinear at the presence of surface elasticity and depend on surface elastic properties. This nonlinear feature can be used for probing the bulk and surface properties by acoustic measurements and designing waves’ guides or filters.