Membrane tension plays various critical roles in the cell. We here asked how fast and how far localized pulses of mechanical stress dynamically propagate through biological lipid bilayers. In both coarse-grained and all-atom molecular dynamics simulations of a dipalmitoylphosphatidylcholine lipid bilayer, we observed nanometer-wide stress pulses, propagating very efficiently longitudinally at a velocity of approximately 1.4 ± 0.5 nm/ps (km/s), in close agreement with the expected speed of sound from experiments. Remarkably, the predicted characteristic attenuation time of the pulses was in the order of tens of picoseconds, implying longitudinal stress propagation over length scales up to several tens of nanometers before damping. Furthermore, the computed dispersion relation leading to such damping was consistent with proposed continuum viscoelastic models of propagation. We suggest this mode of stress propagation as a potential ultrafast mechanism of signaling that may quickly couple mechanosensitive elements in crowded biological membranes.