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Carbon nanotubes (CNT) are considered to be ultra strong and stiff reinforcements for structural composite applications. The load transfer between the inner and outer nanotubes in multiwall carbon nanotubes (MWCNT) has to be clearly understood to realize their potential in not only composites, but also other applications such as nano-springs and nano-bearings. In this paper, we study the load transfer between the walls of multiwall nanotubes both in tension and compression using molecular dynamics simulations. It is found that very minimal load is transferred to the inner nanotube during tension. The load transfer in compression of capped nanotubes is much greater than that in tension. In the case of uncapped nanotubes, the inner nanotube is deformed in bending, only after the outer nanotube is extensively deformed by buckling. It is found that the presence of a few interstitial atoms between the walls of multiwall nanotube can improve the stiffness and enhance the load transfer to the inner nanotubes both in tension and compression.