A methodological approach that is based on a lumped parameter model is proposed for analyzing the dynamic electromagnetic performance of iron-free coil systems with massive conductors. This approach is particularly convenient in studying the transient current density distribution inside the turns and the transient magnetic field distribution in every region outside the coils. It is especially suitable for analyzing air core axisymmetric coils systems. The overall components, including power supplies, can be accurately taken into account. The analytical basis and numerical approach of the method, which has been implemented, and its most interesting features and critical problems are discussed. Some numerical results of practical interest are given.