A method is described for quantitatively reconstructing a spatial inhomogeneity along a one‐dimensional structure from measurements of its resonant frequencies (fundamental and higher modes). A relationship between the shifts in the resonant frequencies of the structure due to a material inhomogeneity (computed relative to the frequencies of the homogeneous state) and the coefficients in a Fourier expansion of the inhomogeneity, which holds to the first order in the material perturbation, is derived. If a number of successive resonant frequencies are excited and measured, the unknown inhomogeneity may then be reconstructed by Fourier summation. The material inhomogeneity recovered by this technique is the sum of the fractional changes in elastic modulus and density. For simplicity, the analysis is carried out in one dimension in the absence of damping. Compared to pulse‐echo methods, the advantages of the dimensional resonance method are that it can image slowly varying impedance variations, can utilize narrow bandwidth detection, has its signal enhanced by the resonantQ, and generally utilizes lower frequencies where problems of attenuation and scattering are less serious.