The transfer-matrix method is suitable for solving modal and spectral characteristics and dynamic deformation and stress analysis of shaft systems with articulated joints. In the article, the authors focus on deriving the transmission matrixes core elements of the dynamic model of the shaft system, namely section continuum of constant annular cross-section, discrete compensation for additional materials and flexible storage. Derived transfer matrixes can be used for the calculation of natural frequencies and models of vibration in the case of natural vibration and steady state vectors of forced vibration in the state of combined bending-gyratory oscillation shaft systems with the dominant elements of the one-dimensional linear continuum.