A bi-directional corrugated sandwich tube structure was proposed, inspired by the front jaw of peacock mantis shrimp. The dynamic responses and energy absorption characteristics of bi-directional corrugated sandwich tubes under inner blast loading were investigated numerically and experimentally. It was found that three typical deformation modes including localized plastic deformation, elliptical plastic large deformation and laceration. The numerical results of the mid-point deflection of the outer tube and the final deformation mode of the structure agree well with the experimental results. Subsequently, the effects of the number of corrugation of the bi-directional corrugated core tube, the inner and outer tube wall thicknesses and TNT dose on its dynamic response and energy absorption characteristics were investigated thoroughly. The results show that the energy absorption ratio of the structure increases first, and then decreases with the increase of the number of corrugation. Increasing the inner tube wall thickness and decreasing the outer tube wall thickness can improve the shock resistance performance. Compared with the inner tube wall thickness of 1.5 mm and an outer tube wall thickness of 2.5 mm, the structure with an inner tube wall thickness of 2.5 mm and an outer tube wall thickness of 1.5 mm can reduce the maximum mid-point deflection (MD) of the outer tube by 67.6% and reduce the mass by 6.0%. As the TNT dose increases, the percentage of energy absorbed by the inner tube decreases gradually, while the percentage of energy absorbed by the core and outer tube increases. Finally, the specific energy absorption (SEA) of the structure and MD of the outer tube were predicted using BP (back propagation) neural network model, PSO-BP (particle swarm optimization-back propagation) neural network model, and RSM (response surface methodology) model to optimize the proposed structure.