Speed resonance of the Cardan coupling shafts is depended on the stiffness of the shaft edges. The paper describes a method to analyze transverse oscillations of the chain of Cardan coupling shafts, i. e. including a clutch and gearbox of the shaft. The method of the imaginary section is applied here to a system of transversely oscillating pliable bodies. The state variables inside the individual shafts are solved using the transfer matrix method. The paper is focused on the determination of the speed resonance of the system.