A numerical analysis of the nonstationary heat and mass exchange in the heat-resistant composite material (a carbon-filled plastic), forming a cover of the conic part of a blunt-nosed body exposed repeatedly to a pulsed laser radiation, has been performed on the basis of the heat model of destruction of such a material. Different regimes of thermochemical destruction of the carbon-filled plastic due to the action of a moderate-intensity laser radiation on it under the conditions where the porous material of the spherical bluntness of the body is not melted were determined. It was established that the gaseous products of pyrolysis of the carbon material as well as its condensed-phase particles and vapor play a dominant role in the shielding of the surface of the conic part of the body from the laser radiation.