Impact of an asteroid on the Earth could be catastrophic. Deflection and fragmentation of such asteroids by surface and underground nuclear explosives has been proposed. The aim of this investigation is the optimization of explosive effects by varying of the explosive depth and charge. The study is based on nonlinear thermomechanics of an elastoviscoplastic damaged medium. For numerical simulation Godunov's type scheme on unstructured grid is used. The deflecting impulse depends on the power and depth of the charge, and the physical and strength properties of asteroid material. The process of dynamical vaporization and disintegration of asteroid material around the burst point as well as the generation of intensive jet is also investigated.