Abstract For damage detection of railway tracks, a two-axle test vehicle is better than a single-axle vehicle due to its capability of self standing and stability. This paper presents a new, comprehensive theoretical framework for a two-axle test vehicle moving over railway tracks modeled as a simply supported beam with elastic foundation. Firstly, closed-form solutions for both the vehicle and rail responses of the system were derived, along with those for the two contact points by a back calculation procedure. Secondly, the driving component of the contact-point response was processed by the Hilbert transform to yield the Instantaneous Amplitude Squared (IAS) for damage detection. Then, the efficacy of the proposed technique was numerically validated by the Finite Element Method (FEM). Particularly, the sensitivity of the proposed technique was investigated against various factors, including the damage severity, multi damages, vehicle speed, track unevenness, track damping, and measurement noise. The result shows that the IAS of the driving component of the contact point response of the railway track is a good damage indicator in that it is of low frequencies and narrow band, while its modal amplitude is sensitive to the stiffness loss in rail supports.