We propose two new methods for solution of the eigenvalue assignment problem associated with the second-order control system Mx(t) + Dx over dot(t) + Kx(t) = Bu(t) P-e(lambda) = lambda(2)M + lambda(D + BF2) + (K + BF1) has a desired set of eigenvalues and the associated eigenvectors are well conditioned. Method 1 is a modification of the singular value decomposition-based method proposed by Juang and Maghami which is a second-order adaptation of the well-known robust eigenvalue assignment method by Kautsky et al. for first-order systems. Method 2 is an extension of the recent non-modal approach of Datta and Rincon for feedback stabilization of second-order systems. Robustness to numerical round-off errors is achieved by minimizing the condition numbers of the eigenvectors of the closed-loop second-order pencil. Control robustness to large plant uncertainty will not be explicitly considered in this paper. Numerical results for both the two methods are favourable. A comparative study of the methods is included in the paper.