Abstract: Brain neural systems and mechanical vibration systems share similar oscillatory behavior. In mechanical systems, oscillation depends on stiffness and damping, where stiffness reflects the amplitude of the system's response to external stimulation, and damping characterizes the decay of the system's state. Although responses and decay also occur in the neural system, it is unclear whether the brain exhibits similar features of stiffness and damping. Using the classical FitzHugh-Nagumo (FHN) neuron model, we proposed a mechanical model for the neuron that includes the state variable of the ion channels' opening probability, as well as nonlinear stiffness and damping. First, we analyzed the dynamic behavior of a single FHN neuron and revealed that negative damping and weak stiffness jointly support the generation of neuron action potentials, while strong damping induces the refractory period. Second, we constructed a mechanical model for the large-scale brain complex network wherein all model parameters were automatically identified via the Bayesian optimization. By analyzing the corresponding principal stiffness and damping of the system, we found that the left hemisphere of the resting brain has lower stiffness and damping compared to the right hemisphere, and that higher-order functional systems exhibit lower stiffness and damping than lower-order functional systems. Then, by varying the global coupling strength, we revealed that moderate stiffness and damping support the functional balance of the resting-state brain. Finally, through the combination of three cognitive tasks and statistical factor analysis, we found that executive control function is associated with lower stiffness and higher damping. These findings illuminate the mechanical properties of the brain neural system through the analysis of a single neuron and brain complex network.