In this paper the authors attempt is made to model mathematically, on the basis of sufficiently complete nonstationary Navier-Stokes equations, the process of laminar flame propagation for a compressible, viscous, heat conducting, combusting gas mixture in a closed pipe with a rectangular cross section under conditions of both zero gravity and an external gravitational field. Combustion is initiated by an instantaneous temperature rise in the pipe frontal wall to the adiabatic combustion temperature. The combustible mixture is one in which an Arrhenius type exothermal combustion regime occurs.