The accurate calculation of the magnetic fields steady or rapidly varying is extremely important in designing pulsed power supplies for controlled thermonuclear fusion experiments, lasers, etc., where the traditional simplifying assumptions become unacceptable - especially when ferromagnetic materials in high magnetic fields are used. A finite element method for solution of Maxwell's equations for a moving media in terms of the magnetic vector potential and electrokinetic scalar potential describing the penetration of the magnetic fields in fast pulsing power supplies of electromechanical type is presented. The formulation for the steady-state magnetic fields in nonlinear media results as a particular case of the method. This approach was used for predicting the discharge parameter for the very fast discharging homopolar machine (FDX) designed by the Energy Storage Group at the University of Texas. FDX is in an advanced state of execution. This work was supported by the Electric Power Research Institute (EPRI) and the Energy Research and Development Administration (ERDA).