Two-dimensional stress waves in an elastic circular cylinder are analyzed numerically, when a variety of axisymmetric impulsive loads are applied to the end face of the cylinder. The effect of the shape of the applied impulsive load on stress wave propagation and on generation of a tensile stress is demonstrated. It is clearly demonstrated that, when the rise time of the applied load is sufficiently short, such as when a charge is detonated on the end face, a large tensile stress is caused along the axis of the cylinder by the wave reflected from the curved surface converging on to the axis, and is caused, along the circle on the end face, by the reflection at the cylindrical surface as a wave of tension. The generation of these tensile stresses explains fairly well the examples of fracture in brittle specimens which were obtained by Kolsky and Shearman, and by the authors. The distribution curves of the caused tensile stress along the axis of the cylinder and along the end face are presented, and are effective in predicting the occurrence of fractures under impulsive loading.