Recent toxicology studies suggest that nanosized aggregates of fullerene molecules can enter cells and alter their functions, and also cross the blood-brain barrier. However, the mechanisms by which fullerenes penetrate and disrupt cell membranes are still poorly understood. Here we use computer simulations to explore the translocation of fullerene clusters through a model lipid membrane and the effect of high fullerene concentrations on membrane properties. The fullerene molecules rapidly aggregate in water but disaggregate after entering the membrane interior. The permeation of a solid-like fullerene aggregate into the lipid bilayer is thermodynamically favoured and occurs on the microsecond timescale. High concentrations of fullerene induce changes in the structural and elastic properties of the lipid bilayer, but these are not large enough to mechanically damage the membrane. Our results suggest that mechanical damage is an unlikely mechanism for membrane disruption and fullerene toxicity.