This paper proposes a newly developed method, which measures absolute axial stress of continuous welded rails (CWR), based on the change of resonant frequency of standing wave mode of rails in the periodic infinite railway track structure. First, the authors theoretically derived dominant simultaneous equations regarding the vibration motions of a three-dimensional Timoshenko-beam under compressive or tensional axial-loadings. By applying the Floquet's theorem to dominant equations of the unit cell, which is an irreducible sub-structure with periodicity of the infinite track structure, the equations are simplified into Eigen-value problems in the frequency domain. Numerical dispersion analyses of wave modes propagating in a track made clear the relation among axial-loadings, wavenumber and natural frequency and provided an evaluation of the feasibility of the proposed method for the measurement of the absolute axial stress. Furthermore, in-situ measurements in the existing CWR track experimentally confirmed the linearity between the axial stress and the resonant frequency.