The basic element for creating computational models of shafts is an one-dimensional linear continuum. Consider the one-dimensional continuum in a state of combined bending-gyratory vibration. Modal and spectral properties of relative lateral vibration in the rotating area are dependent on the angular velocity of shaft rotation. The problem can be after a first approximation solved analytically. More complex systems can be solved either using the finite element discretization method and converting to the problem of eigenvalues, eigenvectors, or using the transfer-matrix method, which is combination of analytical solution and numerical methods. The paper described the use of the transfer-matrix method for solving of one-dimensional linear continuum speed resonance in a state of bending-gyratory vibration. The authors drew a comparison between the results achieved by the transfer-matrix method and the results of the analytical solution.