The specific energy absorbed during uniaxial tension and during axial compression of cylindrical tubes with various wall thicknesses and diameters has been measured for 1015 steel in two heat treatment conditions and for 6061 aluminum alloy in four heat treatment conditions. For axial compression of tubes, the energy absorbed/unit weight, Esc, is a function of the thickness to diameter ratio and the present work shows that for 0.02 < t/D < 0.1, the dependence is well described by a power law of the form Esc = A(t/D)m where m varies between 0.5 and 1.0 for different materials. A salient finding is that the ranking of materials for specific energy absorption depends upon the testing mode. In tension, it is shown that density ρ, ultimate tensile strength σult and the uniform elongation, εu are significant in the ranking of materials. Specifically, the present and previous results show that the energy absorbed/unit weight, depends upon both the ultimate tensile strength σult and the corresponding true (tensile) strains εu , EsT = σult εu /ρ(1 + εu ). In axial compression, however, the measured variations in Esc (for a fixed geometry) with the different materials show that Esc is simply proportional to the specific ultimate tensile strength (σult /ρ). The magnitude of the tensile uniform elongation is unimportant in ranking materials for this compression collapse mode because the geometric instability present in tension tests does not arise in the plastic buckling process that occurs during the axial compression of cylinders.