Nerve outgrowth in the developing nervous system utilizes a variety of attractive and repulsive molecules found in the extracellular environment. In addition, physical cues may play an important regulatory role in determining directional outgrowth of nervous tissue. Here, by culturing nerve cells on filamentous surfaces and measuring directional growth, we tested the hypothesis that substrate curvature is sufficient to influence the directional outgrowth of nerve cells. We found that the mean direction of neurite outgrowth aligned with the direction of minimum principle curvature, and the spatial variance in outgrowth direction was directly related to the maximum principle curvature. As substrate size approached the size of an axon, adherent neurons extended processes that followed the direction of the long axis of the substrate similar to what occurs during development along pioneering axons and radial glial fibers. A simple Boltzmann model describing the interplay between adhesion and bending stiffness of the nerve process was found to be in close agreement with the data suggesting that cell stiffness and substrate curvature can act together in a manner that is sufficient to direct nerve outgrowth in the absence of contrasting molecular cues. The study highlights the potential importance of cellular level geometry as a fidelity-enhancing cue in the developing and regenerating nervous system.