Mechanical tension is a particularly effective stimulus for axonal elongation, but little is known about how it leads to the formation of new axon. To better understand this process, we examined the movement of axonal branch points, beads bound to the axon, and docked mitochondria while monitoring axonal width. We found these markers moved in a pattern that suggests elongation occurs by viscoelastic stretching and volume addition along the axon. To test the coupling between "lengthening" and "growth," we measured axonal width while forcing axons to grow and then pause by controlling the tension applied to the growth cone or to the cell body. We found axons thinned during high rates of elongation and thickened when the growth cones were stationary. These findings suggest that forces cause lengthening because they stretch the axon and that growth occurs, in a loosely coupled step, by volume addition along the axon.