The movement and shaping of the current sheath in coaxial plasma guns is numerically modelled by means of a dynamic finite-elements representation. Numerical instabilities are avoided by a reshaping algorithm applied during the tracking of the current sheath acceleration. Improving upon older versions of the algorithm, the present model includes a delay model to treat the dielectric breakdown. Comparison against experimental measurements showed very good performances in representing the arrival times of the shock front at different filling pressures.