A new method for gradient-based flutter constrained optimization is presented. An evaluation of the aeroelastic phenomenon of flutter through the control of the damping is studied. Through the mathematical formulation of the flutter is created a flutter constraint to pose the basis for a gradient-based structural optimization with as objective the mass objective, and as constraints stress and flutter. The method is intended to be used in a gradient-based analysis which allows solving large optimization in reasonable computational time. Structural optimization methods must provide a solution in a limited time for making effective use of high-performance computing resources. Besides, in adjoint-based gradient methods is necessary to obtain the gradient, with respect to thousands of design variables and this action has a cost similar to the analysis.