The eigenvalue problems of the buckling loads and natural frequencies of a braced beam on an elastic foundation are investigated.The exact solutions for the eigenvalues are presented.The eigenvalues vary with the different parameters and are especially sensitive to the brace location.As the beam of a continuous system has infinite eigenvalues and these eigenvalues are influenced differently by a brace,the eigenvalues show rich variation patterns.Because these eigenvalues physically correspond to the structure buckling loads and natural frequencies,the study on the eigenvalues variation patterns can offer a design guidance of using a lateral brace of translation spring to strengthen the structure.