burning solid fuel, a crack-visible cavity, adhesion power, predestruction zones with bondings between margins. 

The fracture mechanics’ flat stationary problem for the burning deformable fuel weakened by an arbitrarily based system of the crack-visible cavities which surfaces can burn is considered. It is considered that crack-visible cavities have end cavities with bondings between margins and on a border of a fual charge the mixed boundary conditions are set. The problem about balance of the fuel charge weakened by crack-visible cavities is reduced to the decision of nonlinear singular integrated combined equations. According to the solution of this system normal and effort tangents are found in end zones of crack-visible cavities. The local conditions defining stability (safety) of a mode “burning-destruction” mode are received