This article presents an experimental study on the quasi-static crushing performance of carbon fiber reinforced polymer (CFRP) rods consisting of unidirectional carbon fibers wrapped by braided glass fibers. Rods with and without a taper are tested and then inserted in extruded and expanded polystyrene foam and cardboard panels. Hybrid columnar aluminum tube–CFRP rod structures are also tested in all panel materials. These results are compared to those based on glass fiber reinforced polymer (GFRP) rods, GFRP rods in polystyrene foams, and to GFRP rods in cardboard from a previous study. Tapered CFRP rods exhibit progressive crushing behavior with specific energy absorption superior to GFRP rods, with values of 82 kJ/kg and 65 kJ/kg, respectively. Moreover, the highest specific energy absorption (111 kJ/kg) is obtained in hybrid columnar aluminum tube–CFRP tapered rods, exceeding values of aluminum tubes (89 kJ/kg) and equivalent structures containing GFRP rods (102 kJ/kg). Within panels, cardboard produces the largest increase in mean load of CFRP and GFRP rods due to most constraining fiber splaying during crushing, followed by extruded foam, and lastly expanded foam. However, crushing displacement is most restricted in cardboard due to earlier final compaction. The smallest variations in crushing load occur in extruded polystyrene due to greater homogeneity throughout the foam structure.