In this paper we discuss the propagation of Rayleigh type waves in an elastic medium with two horizontal layers overlying a semi-infinite elastic medium above which lies a liquid layer. The upper solid layer is taken to be transversally isotropic the elastic properties of which are given by the strain energy volume density function $$2 W = A(e_{xx^2 } + e_{yy^2 } ) + Ce_{xx^2 } + 2 F(e_{xx} + e_{yy} ) e_{zz} + 2(A - 2 N) e_{xx } e_{yy} + L(e_{yz^2 } + e_{zx^2 } ) + Ne_{xy^2 } .$$