Axial compressive simulations are performed on defective and non-defective multiwalledcarbon nanotubes (MWCNTs) using the molecular dynamics method, and the effectof defects upon the buckling behavior is discussed. In our previous study, changes in atomicstresses in MWCNTs with three layers were evaluated until buckling occurred. That studysuggested that the transition from homogeneous stress distributions to inhomogeneous onesplays an important role in the occurrence of buckling in MWCNTs, though the critical stressesor strains relating to buckling are dependent upon the structure and location of defects. In thepresent study, the atomic elastic stiffness of each atom, Bij , is evaluated to discuss the onsetof local buckling in MWCNTs with five layers. The det(Bij) of all atoms is found to change toa negative value long before buckling occurs, while the second smallest eigenvalues of Bij forsome atoms change to a negative value just prior to buckling. The existence of dense regions ofatoms that have two negative eigenvalues of Bij are found to vary as a function of the defectlocation, and to correspond with onset points of local buckling.