Installation of lightning rods for protection of an object against direct lightning strokes is the recommended conventional practice for more than two hundred fifty years. With rapid progress in electronics and computers, microminiaturization of the electrical circuitry, the secondary effect of the direct lightning stroke into the lightning rod becomes itself a serious threat to the electrical and electronic equipment. The lightning protection system entitled as the Dissipation Array System (DAS) introduced to the market more than thirty years ago prevents lightning strokes to the protected object eliminating the secondary effect of the lightning strike. The stroke preventive action of the DAS is based on the active generation of the local space charge, which helps to suppress the initiation and/or propagation of the upward leader or counter leader from the DAS. In absence of such a leader the strike to the DAS and the object protected by DAS can not occur. Three fundamental physical problems have to be solved in order to obtain the quantitative characteristics of interaction between DAS and a thunderstorm cell and the lightning channel. These problems are: (1) development by the DAS of the non-stationary corona and space charge under influence of the electric field of a thunderstorm cell and a stepped downward lightning leader; (2) the influence of the redistribution of the electric field on the initiation of an upward leader; and (3) the interaction between the local space charge and the stepped downward lightning leader. The paper presents the results of the computer modeling of these processes, which requires less assumptions than an analytical solution and is, therefore, more accurate.