Two-stroke engines used in small applications, in order to fulfill the emission requirements, should be equipped with a direct injection system or pneumatic rich mixture injection system. The FAST system in the Piaggio engines is based on the two-throat carburetor. Till now the Piaggio company has not published the physical processes taking place in such engines. The author has carried out the deep study of the process of rich mixture injection by an additional compressor and the results of calculations are presented in the paper. The simulation was done by using of the own computer program based on the mathematical model taking into account the unsteady gas flow of semi-perfect gas, the changed parameters of engine geometry and controlled parameters. The paper includes description of the fuelling system, mathematical model, calculation algorithm, results of calculations for different controlled parameters and comparison with other systems. The FAST computer program enables to define the characteristics of the cylinder charge, engine power, fuel consumption and exhaust gas composition. The simple mechanical fuelling system without electronic participation enables to apply it for the engines driven the small vehicles. However the drive of the compressor by tooth belt from the engine crankshaft decreases the total engine power about 20%.