The clarification of the sliding behavior between nested walls in a multi-walled carbon nanotube (MWCNT) is crucial for its applications in nano-electro-mechanical systems. The pull-out processes of some outer walls against other inner walls in MWCNTs are studied by molecular mechanics simulations to investigate this sliding behavior between nested walls. The pull-out force for both double-walled carbon nanotube (DWCNT) and MWCNT with more than two walls is found to be proportional to the diameter of the critical wall (i.e., the immediate outer wall at the sliding surface), and independent of nanotube length and chirality. The underlined mechanism for this phenomenon is systematically explored by investigating the interfacial shear stress during the pull-out and the corresponding surface energy density. The importance and necessity of considering MWCNTs with more than two walls are indicated from their higher surface energy densities than that of DWCNT. Furthermore, the obtained result demonstrates that the conventional definition of the interfacial shear strength is inappropriate for the sliding behavior between nested walls in MWCNTs. Finally, a simple universal theory is proposed for the first time to predict the pull-out force for an arbitrary sliding in a given MWCNT, directly from the diameter of the critical wall.