As waves propagate along the waveguide, wave reflections and transmissions will occur when waves are incident upon discontinuities. Based on wave reflection characteristics, a discontinuity locating method is proposed. In order to obtain the amplitudes of the reflection coefficients, a measurement model and a generalized model of the reflection coefficients are developed. It is possible to identify the position of the discontinuities by matching the reflections of the measurement model and generalized model. The effectiveness of the discontinuity locating method is validated by two experiments to locate an added discontinuity and a crack in the beam, with locating errors of 0% and 0.06%, respectively.