As fluids and porous media are compressible, particularly if free gases are present in the fluid and/or at the pore wall, the permeability of such media varies as a function of the fluid pressure. Under high fluid pressure the permeability increases and under low pressure it decreases. Mechanical vibrations discharged into porous media make the fluid pressure vary and, thus, cause flow by vibration which is directed out of the vibration source. With regard to the specific use of mechanical vibrations for soil remediation methods or injection techniques, for example, a Darcy equation based theory and the fundamental principles of such flows are presented. Hereby, the permeability included in the Darcy equation is a pressure-dependent parameter. The stationary pressure line equation and, in the case of a sine vibration, the equation of the time averaged Darcy velocity are given as a function of the gas content in the fluid and at the pore wall.