This work demonstrates a robust approach for computing complex wave numbers and amplitudes of waves in structures from experimental or numerical data. The approach postulates a wave field, which is a linear combination of damped waves. The number of waves and initial estimates of the complex wave numbers are based on any apriori physical knowledge and on the results of standard analyses of the data, such as wave-number transforms and spatial attenuation rates. Given these initial estimates of wave numbers, associated wave amplitudes are computed by linear least-squares inversion to data. Optimization algorithms improve these estimates by searching for complex wave numbers and amplitudes that minimize the normalized mean-square error between the data and the wave field. This approach is often more robust than Prony-based techniques, which require equally spaced data and are more sensitive to noise or unmodeled components. The approach is demonstrated on experimental vibration measurements of a damped box beam. Loss factors are computed for traditional flexural waves as well as plate waves, which involve flexural motions of the walls of the box beam. [Work supported by ONR.]