The axial stiffness of MWCNTs is demonstrated to be determined only by several external shells (usually 3-5 and up to 15 for the extremely large nanotubes and high elongations) what is in a good agreement with experimentally observed inverse relation between the radius and Young modulus (i.e., stiffness) of MWCNTs. This result is a consequence of the van der Waals intershell interaction. The interpolating formula is obtained for the actual axial stiffness of MWCNT as a function of the tube external radius and elongation.