A. G. Shatalov UDC 536.2.01 Consideration is given to a three-dimensional problem of heating of a half-space by the Gaussian energy flux with allowance made for the heat-flux inertia. It is assumed that the ablation front is formed at the points at which the temperature is equal to the melting temperature and the Stefan condition is satisfied. The mechanism of removal of mass is not considered. Using the ray method and taking into account three expansion terms, an ablation-surface equation and temperature have been obtained. Account for the inertia of the heat flux leads to the fact that the ablation-front velocity at the initial instant of time is finite. The condition for the onset of ablation of the material at the initial instant of time has been obtained. The solutions for the fronts of ablation and temperature are illustrated by the graphs. Voronezh Military Aviation Engineering Institute, Voronezh, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 76, No. 5, pp. 25-29, September-October, 2003. Original article submitted January 29, 2002; revision submitted March 19, 2003.