Surface permeability of saturated porous half spaces can influence the presence of surface waves, i.e. Rayleigh and/or Stoneley waves, as well as behaviour of these waves. Rayleigh waves exist in the porous half space with permeable surface, while there are both Rayleigh waves and Stoneley waves for the case of the impermeable surface. Rayleigh and Stoneley waves play important roles in engineering prospecting and acoustic testing, respectively. Therefore, it is necessary to investigate effects of the surface permeability on behaviours of these waves. In this paper, the root searching algorithm of the frequency equations of surface waves is transformed into the eigenvalue problem using thin layer method. According to the behaviour of attenuation of the surface waves along depth direction, the eigenvalues and eigenvectors corresponding to the surface waves can be sifted from the calculated ones. The frequency behaviour i.e. dispersion and attenuation can be calculated from the sifted eigenvalues. The variations of the fluid pressure and skeleton displacements with the depth can be obtained from the corresponding eigenvectors. The influence depth and extent of Rayleigh and Stoneley waves are then analyzed based on those variations for the case of the impermeable surface.