We present here a thermodynamic model for tension and compression forces within axons (neurites) of the specific neural-cell line, PC 12, which seems generally applicable to neuronal growth. We suggest that these forces play a crucial role in microtubule assembly during axonal elongation. The Gibbs free energy change for the axonal elongation phase of neuronal growth is modeled as the sum of the extensional work for pulling on a random actin network, work of assembly for compressed microtubules and surface energy terms. This model explains the results of previously published experiments concerning axonal stability and microtubule polymerization and has been used to predict other phenomena.