A scheme for computer simulation of a negative stepped leader is developed, based on a physical description of the processes occurring during step development. The scheme is applied to a three-dimensional model of the interaction between a downward negative leader and a grounded mast under two assumptions, one with and one without an upward positive leader initiated from the tip of the mast. The modeling is performed for 2-m and 10-m-diameter leaders under a -10-MV and -40-MV electrical potential, respectively. The downward leader reacts to the mast only at the final jump-over, irrespective of the emission of the positive leader from the mast, thus suggesting the critical role of the final jump. The dominant factor in the interaction of the negative leader with a grounded mast of fixed height is shown to be the leader's potential, which determines the length of the leader step and, thus, the length of the final jump to the ground structure. ¿ 2000 American Geophysical Union