The applicability of matched-field processing (MFP) [Baggeroer et al., IEEE J. Ocean. Eng. 18, 401--424 (1993)] techniques to localize sources of vibration in structures and to perform nondestructive testing is explored. MFP is a generalized procedure of array processing used in ocean acoustics to either localize sources or perform inversions. MFP involves correlations between the solutions (or ``replicas'') of the wave equation for a given acoustic model of the ocean and the data measured at an array of sensors. The correlations are made using an assortment of linear and nonlinear methods. These techniques were successfully tested using simulation for the relatively simple problem of localizing a harmonic point force on a simply supported laterally vibrating beam. Wave equation solutions for describing the vibration of more complicated structures (simulated by adding spring constraints to the beam) become, at some point of complexity, intractable. Often statistical techniques provide the only practical description of such structural vibration problems. Multiple constraint MFP methods, tolerant to solution mismatch, were used to deal with these more complicated structures. Finally, it was demonstrated that MFP methods might also be used as a means of nondestructive testing in order to locate defects.