Voltage-induced swelling of action potential (AP) accompanies shrinkage along the tubular axon. Longitudinal tensions appear at both boundaries of AP of nerve axon, and the line tension at the front boundary has been shown to be greater than that at the rear boundary. The difference of tensions has been certified by previously observed diphasic heat behavior of AP. The propagation velocity of AP is determined by the balance between the difference of tensions and the hydrodynamic resistance of AP by ambient water. The bilayer lipid membrane is liberated from the strong electrostriction of resting potential to depolarized AP. An elastic model of both boundaries of AP has been proposed, which describes the relation between diphasic heat behavior of AP and generated line tensions. The propagation velocity of HEK-293 cells, squid giant axon (SGA), and garfish olfactory nerve (GON) has been analyzed and reliably explained by the proposed line tension model. The energy cost of propelling APs of SGA and GON has been shown to be greater than that of the electric energy.