Novel auxetic tubes (NAT) were designed, fabricated and examined. Their mechanical properties were compared with the original auxetic tube (OAT) by the finite element method and experiments. The results show that NAT increases the specific energy absorption (SEA) without sacrificing the auxetic characteristic. Then, the effect of unit cell parameters on the mechanical properties of NAT tubes was explored. The results show that, in a certain range, rib reduction can improve the SEA of NAT without sacrificing the auxetic effect. To further improve the mechanical properties of NAT, three novel ribbed auxetic tubes (NRAT) were proposed and compared with NAT. It is concluded that the SEA of NAT can be improved by adding a straight rib to the inner long axis of the ellipse. In addition, the effect of straight rib width on the mechanical properties of NRAT was investigated. The results show that the larger the straight rib is, the higher the energy absorption is. Finally, the stability of the 3D auxetic tubular metamaterial is greater than that of the 2D auxetic thin-plate metamaterial by investigating. Due to their desirable mechanical properties, the NAT and NRAT have great potential for applications in medical engineering, vehicle crashworthiness and protective infrastructure.