A method and system for inspecting a rail by guided waves, the rail being instrumented by sensors. The method comprises the steps of receiving elastic wave measurements from one or more sensors, as a train passes, releasing energy as guided waves into the rail; and of determining a function representative of the impulse response of the rail and the sensors. Developments describe how to determine the existence, position and characterisation of a defect in the rail (e.g. fracture, incipient fracture, etc.), the use of inter-correlation analyses, correlation of the coda of correlations, Passive Inverse Filter, imaging techniques. Other aspects are described for exploring rail defects: sensor position and movement, acquisition time, sampling frequency, frequency filters, amplifications, techniques for learning during successive train passes, signal injection by transducers. Software aspects are described.