The behaviors of concentric-double inclusions dispersed in continuous media are investigated theoretical-ly to find some possibilities of improving toughness of composite materials by dispersing double-inclusions instead of single-inclusions. The general solutions of the Stokes equation, expressed in terms of the spherical harmonics, are used for analyzing the problems that are related to the concentric-double inclusions. From the analysis, it is found that the pressure and stress fields inside and outside the inclusion can be modified by changing the modulus rations and the thickness of shell layer. Especially, the positions of the minimum pressure points and the maximum stress points turn out to be controllable with some degree of freedom.