Libyan Desert Glass contains meteoritic material and, therefore, its origin is most likely associated with an impact event. However, the impact crater has not been found. We performed numerical simulations of impacts of stony and cometary bodies in order to confirm the version that this glass was formed from silica heated by radiation from aerial bursts near the ground. Asteroids were treated as strengthless bodies from dunite with a density of 3.3 g cm À3 , and comets as icy bodies with a density of 1 g cm À3 . The simulations based on hydrodynamic equations included the equations of radiation transfer. Melting and vaporization of a silica target under action of radiation incident on a planar surface were modeled using a one-dimensional hydrodynamic equation of energy and equations of radiation transfer in two-flux approximation. We selected those variants of simulations in which a crater is not formed, a fireball touches the earth surface, and the area of a molten target corresponds to the area of the Libyan Desert Glass strewn field. Appropriate options include the impact of an asteroid with a diameter of 300 m, an entry speed of 35 km s À1 , and an entry angle of 8°, and cometary bodies with diameters from 150 to 300 m, speeds of 50-70 km s À1 , and entry angles from 15°to 45°. Impact options with crater formation are also discussed. The maximum depth of molten silica at ground zero reaches 10 cm with the cometary impacts and 3-4 cm with the asteroidal impact. Melting occurs during a period of time from 50 to 400 s.