Nanoindentation is a promising technique for deducing the elastic property of carbon nanotubes (CNTs). The paper presents an atomistic study on the nanoindentation mechanisms of single-walled and multiwalled CNTs and CNT clusters, through which the deformation characteristics are linked with CNT elastic stiffness. The assembly of individual single-walled CNTs (SWCNTs) into multiwalled CNTs (MWCNTs) and CNT clusters would significantly increase the buckling resistance in terms of withstanding the indentation load. Reverse analysis algorithms are proposed to extract the CNT stiffness by utilizing the indentation force-depth data measured from the prebuckling regimes. The numerical studies carried out in this paper may be used to guide the nanoindentation experiments, explain and extract useful data from the test, as well as stimulate new experiments.