Significance Recent experimental studies report correlations between carbon nanotube toxicity and tube length and stiffness. Very little is known, however, about the actual behavior of these fibrous nanomaterials inside living cells following uptake, and the fundamental mechanistic link between stiffness and toxicity is unclear. Here we reveal a nanomechanical mechanism by which sufficiently long and stiff carbon nanotubes damage lysosomes, a class of membrane-enclosed organelles found inside cells that are responsible for breaking down diverse biomolecules and debris. The precise material parameters needed to activate this unique mechanical toxicity pathway are identified through coupled theoretical modeling, molecular dynamics simulations, and experimental studies, leading to a predictive pathogenicity classification diagram that distinguishes toxic from biocompatible nanomaterials based on their geometry and stiffness.