In this paper the robustness of a spectral assignment method applied to the system of a flexible beam is studied. It is shown that the intersection between any admissible set of closed-loop eigenvalues of the nominal system and a corresponding set of a perturbed system can only have a finite number of elements. Then, the impact on the eigenvalues of the perturbed system of a control law that affects only a finite number of eigenvalues of the nominal system is investigated. It is proved that only a finite number of eigenvalues of the perturbed system is moved. In addition, the polynomial whose roots are these closed-loop eigenvalues of the perturbed system is determined. Finally, using a new parameterization of uncertainty, the nonlinearity of the coefficients of this polynomial with respect to the uncertain parameters is simplified, turning it into a multivariate polynomial form whose stability robustness can be studied using several known methods.