A numerical method to simulate the high-speed free forming of a clamped circular disk in an electromagnetic forming system using a flat spiral coil is presented. The method combines field penetration into the disk and dynamic elasto-plastic deformation of the disk. The spiral coil is approximated by coaxial circular loops carrying the discharge current from a capacitor bank. The penetration of the magnetic field of the coil into the disk is formulated as a boundary-value problem for the diffusion equation. Magnetic field, eddy currents and electromagnetic force density in the disk are calculated. An equation of motion for the disk loaded by the magnetic force is combined with the field equation as well as an equivalent circuit equation. Plane stress condition is assumed. Strain-rate effect on the work-hardening law of the disk material is taken into account. An experiment on the free bulging of annealed aluminum disks is also presented, showing fairly good agreement with the numerical solution.