We consider the problem of minimizing the fuel consumption of subsonic passenger and transport aircraft at the cruise flight phase. An optimization problem is stated to form the altitude and speed flight profile. It is proposed to solve this problem by the coordinate descent method (taking into account the constraints) combined with the use of a set of auxiliary candidate points. The calculation of fuel consumption as an objective function of optimization is realized by numerical modeling with a fixed step for speed and altitude transients and by a simplified calculation of the per second consumption based on the static equations on flight intervals with constant speed and altitude.