The mechanical behavior of self-assembled lipid tubules is an important property which determines their suitability for technological applications. We study the instability of multibilayer lipid tubules (with wall thickness t and external radius R(ext)) beyond elastic response under local radial atomic force microscopy indentations. A discontinuity in force-distance curves associated with the buckling instability of lipid tubules is observed. The critical force at which lipid tubules undergo a buckling transition linearly scales as t/R(ext). In addition, a reduced critical buckling force is found to extend a distance of similar to 1 mu m from the end of lipid tubules