The effect of stress transfer within double-walled carbon nanotubes upon their ability to reinforce composites has been reported. The level to which stress can be transferred between the different layers or walls in multiwalled carbon nanotubes (MWNT) is of profound significance for their ability to reinforce a matrix. The double multiwalled carbon nanotubes (DWNT) samples were prepared starting from commercial SWNT materials prepared via the electric-arc method (NANOCARBLAB). It has been found that the stress transfer from the outer to the inner walls in DWNT in composites is poor, such that the inner walls are virtually unstressed during both tensile and compressive deformation. The implication of this finding is that the effective Young's Modulus MWNT in composites will be relatively low. The pressurization involves only the hydrostatic component of the stress tensor, which deforms both the inner and outer walls equally.