Abstract: This paper concerns the structure of inside and outside cylindrical shells with packing material between the two shells. Due to the eccentricity of the inside shell, there will be relative slippage between the inside & outside cylindrical shells and the pack material when the shells are subjected to transverse impulsive. After giving the kinetic equation of the structure, the mechanism of the relative slippage is fully analyzed, including the reason of the slippage, the effect on the slippage of mechanical factors such as the enclasping force, the eccentricity, the elastic inertia and rotary inertia of the packing and the impulsive load. Numerical results of an example, which prove the correctness of the theoretical analysis, are also presented. At the end of the paper, suggestions are given to control or avoid the relative slippage.