The interest in Stoneley waves in wellbores drilled through porous media comes from the dependence of its attenuation on formation permeability. This property makes the Stoneley waves an important tool for measuring the permeability of the porous medium [Xianyun, Hezhu, 2007; Dorovsky V. et al. 2010]. Drilling technology induces mudcake buildup between the borehole fluid and the porous formation with permeability of the latter being our main subject of this paper. Therefore what are the distinguishing properties of mudcake buildup during the permeability-measuring process while using the Stoneley wave properties, and what influence does mudcake thickness and rheology have on the attenuation length? There seems to be no obvious answer to these questions. Another important fact is dependence of the characteristics of the radial oscillations of the borehole fluid on formation permeability [Dorovsky et al. 2010; Dorovsky V. et al. 2012]. This fact allows one to measure formation permeability, and it should be evaluated for the case of mudcake presence. An issue of changes in the measuring procedure for permeability in the presence of radial oscillations of the borehole fluid arises in case of radial oscillations. The main property of radial oscillations is the dependence of the relative velocity of the formation matrix and formation fluid on the permeability of the porous medium at the interface between the media. Measuring the relative velocity at the interface between the media on the borehole side, one can use this dependence to calculate formation permeability. In the presence of mudcake, relative velocity dependence on permeability is retained, but only between the formation and mudcake, which cannot be measured directly on the side of the "mudcake-borehole fluid" interface. However, because the relative velocity in the formation beyond the borehole retains its dependence on permeability, it serves as a means of effective attenuation of borehole fluid waves. This can also serve as a tool for measuring formation permeability in the presence of mudcake and seems to be the foundation for numerical attenuation studies of the Stoneley waves and radial waves in the presence of mudcake. Therefore it should be noted that the influence of mudcake on the Stoneley waves was investigated by Liu, Maximov, etc. [Liu, Johnson, 1997; Maximov, Merkulov, 2002] drew the conclusion based on the theoretical analysis within the framework of the Biot theory that mudcake appears to reduce the influence of permeability on the attenuation length of the Stoneley waves.