Hierarchical multi-cavity tubes (HMTs) represent an emerging class of bio-inspired energy-absorbing structures capable of improving crashworthiness through coordinated multi-level deformation. This study presents a computational investigation of HMTs with integrated axial and radial thickness grading under equal-mass constraints. A validated finite element modelling approach is employed to examine progressive collapse behaviour and quantify crashworthiness indicators, including specific energy absorption (SEA), peak crushing force (PCF), and crushing force efficiency (CFE). The results show that increasing hierarchical order significantly enhances energy absorption performance by promoting multi-path folding mechanisms. Under equal-mass conditions, the third-order configuration achieves a maximum SEA of 38.79 J/g and a CFE of 0.87, representing an improvement of approximately 19.5% compared with non-hierarchical designs. Axial thickness grading effectively reduces PCF while maintaining comparable SEA by enabling sequential deformation along the tube length. Radial thickness grading further improves deformation stability and increases SEA by up to 14.1% without inducing a significant rise in PCF. An analytical model is also developed to predict MCF, showing good agreement with numerical simulations. These findings demonstrate that HMTs with functional thickness grading provide an effective computational design strategy for high-performance crashworthy structures.