In this paper, the finite element equations for the time-domain numerical analysis of transient dynamic axisymmetric problems are newly presented. which are based on the equations of motion in convolution integral as in the previous paper. A hollow cylinder subjected to a sudden internal pressure is solved first as a benchmark problem and then the dynamic stress concentrations are analyzed in detail far hollow cylinders having inner and outer circumferential grooves subjected to sudden internal or axial loadings, all the computed results are compared with the existing or the computed ones obtained by using the commercial finite element packages Nastran and Ansys to show the validity and capability of the presented method.