ABSTRACTA numerical method for solving distributed parameter structural optimization problems in which repeated eigenvalues may occur is formulated. Recent results on directional differentiability of repeated eigenvalues are used to develop a generalized steepest descent method for structural optimization. The algorithm is shown to overcome technical difficulties associated with nondifferentiability of repeated eigenvalues. The method is used to optimize design of a clamped-clamped column in which a repeated eigenvalue occurs.