The quality of an axial compressor depends on the initial design stage-level one-dimensional gas-dynamic calculations. Therefore it means the aim of designers to use at this stage certain experience in successful compressors previously created. It is developed the new design method of running parts of multistage axial compressors – the kinematic modeling method. Its core is that for designing a new compressor it is used kinematics of good compressor prototype. We have obtained the basic formula that underlies the design of gas-dynamic calculation of the flow part of multi-stage axial compressor. The kinematic modeling method is implemented as a computer program. The results from this program showed that basing on the kinematics of the flow in the flow part of the compressor prototype one can design variants of compressors with different indicators and choose the best option.