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 focusing on deriving the transfer matrices of basic elements of the shaft system dynamic model, namely continuum section of constant annular cross-section, and additional material and flexible storage discrete substitution. The derived transfer matrices can be used for calculations of natural frequencies and vibration shape in case of natural vibration and steady state forced vibration vectors in state of combined bending-gyratory vibration of shaft systems with dominant elements of an one-dimensional linear continuum.