The objectives are to present a method for eigenvalue and eigenvector approximate analysis in the presence of repeated eigenvalues and to present an alternate method for the eigenvector sensitivity equations. The method developed for approximate analysis involves a reparametrization of the multivariable structural eigenvalue problems in terms of a single positive-valued parameter. The resulting equations yield first-order approximations of changes in both the eigenvalues and eigenvectors associated with the repeated eigenvalue problem. Examples are given to demonstrate the application of such equations for sensitivity and approximate analysis.