Sandwich structures have superior mechanical properties to be applied in civil, marine, mechanical and aerospace engineering fields. Auxetic structures with negative Poisson's ratio (NPR) can contract laterally when compressed axially to be excellent fillers for the sandwich structures to improve the energy absorption performance. In this work, a cylindrical sandwich filled with double arrowed auxetic structure is proposed. An analytical model is established to predict the dynamic responses of the sandwich structure under axial impact loading. The theoretical model is composed of three parts: energy dissipated due to the auxetic filler, the thin walled tubes, and their interaction. Numerical simulations are performed to validate the theoretical model and the results indicate that the theoretical model proposed is accurate to predict the crushing platform stress of the cylindrical sandwich under axial impact loading.