In the course of the development of the nervous system, neuronal cells extend (grow) axons, which navigate over distances of the order of many cell diameters to reach target dendrites from other neurons and establish neuronal circuits. Some of the central challenges in biophysics today are to develop a quantitative model of axonal growth, which includes the interactions between the neurons and their growth environment, and to describe the complex architecture of neuronal networks in terms of a small number of physical variables. To address these challenges, researchers need new experimental techniques for measuring biomechanical interactions with very high force and spatiotemporal resolutions. Here we report a unique experimental approach that integrates three different high-resolution techniques on the same platform—traction force microscopy (TFM), atomic force microscopy (AFM) and fluorescence microscopy (FM)—to measure biomechanical properties of cortical neurons. To our knowledge, this is the first literature report of combined TFM/AFM/FM measurements performed for any type of cell. Using this combination of powerful experimental techniques, we perform high-resolution measurements of the elastic modulus for cortical neurons and relate these values with traction forces exerted by the cells on the growth substrate (poly acrylamide hydrogels, or PAA, coated with poly D-lysine). We obtain values for the traction stresses exerted by the cortical neurons in the range 30–70 Pa, and traction forces in the range 5–11 nN. Our results demonstrate that neuronal cells stiffen when axons exert forces on the PAA substrate, and that neuronal growth is governed by a contact guidance mechanism, in which axons are guided by external mechanical cues. This work provides new insights for bioengineering novel biomimetic platforms that closely model neuronal growth in vivo, and it has significant impact for creating neuroprosthetic interfaces and devices for neuronal growth and regeneration.