The article substantiates the necessity of designing an optimal gas generator of a gas turbine engine. The generator is to provide coordinated joint operation of its units: compressor, combustion chamber and compressor turbine with the purpose of reducing the period of development of new products, improving their fuel efficiency, providing operability of the blades of a high-temperature cooled compressor turbine and meeting all operational requirements related to the operation of the optimal combustion chamber including a wide range of stable combustion modes, high-altitude start at subzero air and fuel temperature conditions and prevention of the atmosphere pollution by toxic emissions. Methods of optimizing the parameters of coordinated joint operation of gas generator units are developed. These parameters include superficial flow velocities in the boundary interface cross sections between the compressor and the combustion chamber, as well as between the combustion chamber and the compressor turbine. The effective efficiency of the engine thermodynamic cycle is the optimization target function. The required depth of the turbine blades cooling is a functional constraint evaluated with account for calculations of irregularity and instability of the gas temperature field and the actual flow turbulence intensity at the blades’ inlet. We carried out theoretical analysis of the influence of various factors on the gas flow that causes changes in the flow total pressure in the channels of the gas generator gas dynamic model, i.e. changes in the efficiencies of its units. It is shown that the long period (about five years) of the engine final development time, is due to the necessity to perform expensive full-scale tests of prototypes, in particular, it is connected with an incoordinate assignment in designing the values of the flow superficial velocities in the boundary sections between the gas generator units. Designing of an optimal gas generator is only possible on the basis of an integral mathematical model of an optimal combustion chamber.