In this work, perturbation method and Padé approximants are used to compute the eigenvalues of linear problems. This algorithm is based on the introduction of perturbation loads in the eigenvalue problem. This modified problem is solved by using the perturbation method and the Padé approximants. The computation of the eigenvalues consists then on finding the roots of the numerator of a rational fraction. To demonstrate the efficiency of the proposed method, examples of linear vibrations of plates and shells are considered. The obtained results showed that the proposed method can deal with problems with close or multiple eigenvalues. Furthermore, the results also showed that the proposed algorithm is less sensitive to the ill-conditioning of the matrices.