Abstract: Using the theory of elastic wave in porous media, a solution for the radial sound field with a local impulse acoustic source in a fluid-filled borehole surrounded by a fluid-saturated porous formation is found. A numerical evaluation of the full waveform curves of the acoustic pressure is given for different porosities and coefficients of permeability K(k/η). The effect of the permeable formation on sound propagation is discussed. The result of analysis shows that the travel time of the refracted arrival of the longitudinal wave has a linear relationship with porosity over a fairly broad range, it has nothing to do with the variations of frequencies and coefficient of permeability. This provides a theoretical basis for the travel time-porosity acoustic logging based on the time-average equation. The variation of amplitude of Stoneley wave is sensitive both to porosity and coefficient of permeability, its strong attenuation is a feature that makes it different from a homogeneous formation. This may be a useful information to acoustic logging.