When an excessive axial compressive load is applied to a thin-walled stepped circular tube, collapsing occurs locally at the stepped position. Thereafter, the portion with a smaller diameter intrudes into the portion with a larger diameter. Such deformation is developed under almost constant load. In this paper, using results of the elasto-viscoplastic properties for the materials, the authors dealt with this problem theoretically as being one of a large deformation with elasto-viscoplastic properties, and performed numerical analysis by the finite element method and the direct time integration method. The experimental apparatus was the block to block type impact testing machine. Characteristics of the load-deformation relation are studied for three kinds of configuration of the test pieces. Thus, the collapsing characteristics of stepped circular tubes due to the impact axial load were made clear.