A method is presented for locating discontinuities in a uniform waveguide from two or more point frequency response functions (FRFs). The phase of the FRF exhibits modulation when plotted against wavenumber because of interference of waves reflected from the discontinuity, and this is related to the distance of the excitation point from the discontinuity. Such discontinuities might be known boundaries or unknown damage sites. An inverse Fourier transform is used to transform from the wavenumber domain to the spatial domain in order to extract the locations of the discontinuities. The use of the transform relies upon knowledge of the dispersion relation for the waveguide. Experimental results are presented for several uniform isotropic beams which were damaged to differing extents by sawing transverse slots in them. The results show the method to be successful in locating the slots.