Impacts of cosmic bodies (stony and comet-like) are considered that “burn out” (or, more strictly, totally evaporate) in the atmosphere, which do not form craters but cause fires and destruction on the Earth’s surface. The heights of fragmentation, total evaporation, and deceleration of stony and comet-like meteoroids of different sizes, initial velocities, and impact angles are found from numerical simulations. The possible consequences of such falls are considered. The possible parameters of the Tunguska cosmic body are estimated.