Most methods used to update dynamic structural models use either frequency response data or both eigenvalues and mode shape data. This paper presents a technique to adjust the parameters using eigenvalues alone. Eigenvalues may be measured very accurately whereas mode shapes often contain substantial errors. The structure and its theoretical model are perturbed by adding mass or stiffness. The measured eigenvalues before and after each mass or stiffness addition are used to update the parameters by sensitivity analysis. It is shown that with error-free data and a proper choice of the perturbing coordinates, exact parameters can be identified from eigenvalues alone using unconstrained optimization. Due to measurement errors and possible inaccuracies in the structure of the model matrices, the parameters of a real structure are adjusted by incorporating a constraint of minimum changes from the initial estimates using a Bayesian estimator.