In the paper, the statistical modeling method of the lightning attachment process to extended objects has been proposed. The modeling takes into account the probabilities of lightning occurrence with current of different am- plitudes, and nonlinear variation of spark resistance at leader channel growth. The method also takes into considera- tion the dependency of velocity and acceleration of a lightning leader on its potential. The propagation of lightning channel towards the earth is tortuous and random in orientation and does not depend upon ground objects until it en- ters into ＂last stroke zone＂. It assumes that the lightning leader channel orientation begins when its streamer zone touches the earth, a grounded object, a grounded lightning rod or a streamer zone of the ascending leader. The proba- ble frequency of lightning strikes to an investigated object can be obtained by the summation of the total probable number of strikes of all possible potentials at each node of the object, appearing with the assigned probability, as well as the points of origin of the heads of lightning leaders from all nodes on the plain （over the object） at corresponding heights. The proposed method is implemented to ealculate the lightning stroke probability to a high voltage substation. Due to lightning attraction from the territory greater than that of the investigated object, the total number of annual probable lightning strokes to the object is increased by 1.28 times in comparison with the case of the same flat territory.