Two-dimensional stress waves in an elastic/viscoplastic circular cylinder were analyzed numerically, when axisymmetric impacts with various impact velocities were applied to the end face of the cylinder. For the numerical analysis, the finite difference method along bicharacteristics was employed. By obtaining the numerical results, it is demonstrated that, near the impact face, the dynamic stress-strain relation differs clearly with each point even if on a same cross section of the cylinder. Conversely, the bounds of the area near the impact face were obtained at which the dynamic behavior becomes practically uniform. It is also shown that local stress concentrating parts are apt to be formed in the cylinder where a tensil stress arises.