A method of analysis which permits the computation of electromagnetic fields directly in the time domain using the finite element method (FEM) is presented. The method considers coaxially-driven axisymmetrical structures. A new way of implementing absorbing boundary conditions for the coaxial feed is discussed. The method has been successfully used to model coaxially-driven axisymmetrical monopole antennas for a Gausssian pulse excitation. Generally, the results obtained shea good agreement with the previously published numerical and experimental data.