We have studied the conditions of through passage of asteroids with diameters 200, 100, and 50 m, consisting of three types of materials – iron, stone, and water ice, across the Earth’s atmosphere with a minimum trajectory altitude in the range 10–15 km. The conditions of this passage with a subsequent exit into outer space with the preservation of a substantial fraction of the initial mass have been found. The results obtained support our idea explaining one of the long-standing problems of astronomy – the Tunguska phenomenon, which has not received reasonable and comprehensive interpretations to date. We argue that the Tunguska event was caused by an iron asteroid body, which passed through the Earth’s atmosphere and continued to the near-solar orbit.