The optimization of scaffold mechanical properties for neurite extension is critical for neural tissue engineering. Agarose hydrogels can be used to stimulate and maintain three-dimensional neurite extension from primary sensory ganglia in vitro. The present study explores the structure–function relationship between dorsal root ganglion (DRG) neurite extension and agarose gel mechanical properties. A range of agarose gels of differing concentrations were generated and the corresponding rate of E9 DRG neurite extension was measured. Rate of neurite extension was inversely correlated to the mechanical stiffness of agarose gels in the range of 0.75–2.00% (wt/vol) gel concentrations. In addition, we postulate a physical model that predicts the rate of neurite extension in agarose gels, if gel stiffness is a known parameter. This model is based on Heidemann and Buxbaum's model of neurite extension. These results, if extended to scaffolds of other morphological and chemical features, would contribute significantly to the design criteria of three-dimensional scaffolds for neural tissue engineering.