The main characteristics of the long-boom electric antennas installed on board the Cluster satellites are derived from finite element modeling in a kinetic and isotropic space plasma, in the frequency range of about 1–100 kHz. The model is based on the surface charge distribution method in quasi-static conditions. The impedances of both types of antenna, i.e., the double-wire and the double-probe, are computed versus the frequency normalized with respect to the local plasma frequency and for several different Debye lengths. Most of the code outputs are checked using analytic estimations for better understanding of the involved physical mechanisms. As a by-product, the effective length of the double-probe antenna and the mutual impedance between the two antennas are computed by the code. It is shown that if it had been possible to implement such measurements on board, one would have been able not only to determine accurately the electric characteristics of the antennas but also to estimate the local plasma parameters. Nevertheless, an interesting feature predicted by the model has been checked recently in orbit by running a special mode of operation for testing the mutual impedance measurement. The preliminary results are globally consistent with the predictions, except that they suggest that our Maxwellian model for the electron distribution should be revised in order to explain the unexpected low-frequency response. After analysis of the electron flux measurements obtained simultaneously, it appears that a rough adjustment of the electron distribution with a two-component distribution allows us to account for the observations.