In this study, the assignment and theoretical investigations of the problems of forest fire initiation were carried out, including development of a mathematical model for description of heat and mass transfer processes in overterrestrial layer of atmosphere at crown forest fire initiation, taking into account their mutual influence. Mathematical model of forest fire was based on an analysis of experimental data and using concept and methods from reactive media mechanics. In the context of the general mathematical model of forest fires, this study gives a new mathematical setting and method of numerical solution of a problem of a forest fire modeling. The boundary-value problem is solved numerically using the method of splitting according to physical processes. In this paper the assignment and theoretical investigations of the problems of forest fire initiation are carried out.