Rubber is considered as a new material for making landing gear shock absorbers for new energy electric aircraft. This investigation tested nitrile butadiene rubber blocks with different hardness at different loading rates to determine their stress-strain relationships. The mechanical behaviors of rubbers are predicted via an artificial neural network model for the first time. A self-adjusting particle swarm optimization was proposed to optimize the artificial neural network's weights and thresholds with the inertia factors and learning factors automatically adjusted. The number of neurons was optimized. The results revealed that the Young's modulus of the rubber increases with the increasing strain. With larger hardness and a larger strain rate, both the Young's modulus and its increasing rate become larger. The proposed self-adjusting particle swarm optimization improves the accuracy and the convergence speed. With the optimal number of neurons, the proposed artificial neural network has a mean square error of 1.611 × 10⁻⁴ in predicting the stress-strain relationships of the rubber. Compared with traditional artificial neural network models and an artificial neural network optimized by a traditional particle swarm optimization, the proposed model increases the accuracy by 56.5% and 26.5%, respectively. It is an initial attempt to account the coupling effect of the hardness and the strain rate in the rubber constitutive model.