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To ensure ride comfort, the dynamic characteristics, such as natural frequencies, of a vehicle is often tuned to a specific value by managing the magnitude and location of some masses and/or configuration of stiffeners without sacrificing the structural strength and overall fuel performance of the vehicle. We first formulate the mathematical statement of the problem in a constrained eigenvalue form. Optimal solutions are sought using various finite element techniques. A novel methodology involving genetic algorithm and Newton’s iterative method is developed to solve the constrained eigenvalue problems. Several examples, including discrete and continuous systems, are presented to demonstrate the effectiveness and accuracy of the proposed methodology. The strategy of managing the mass location and distribution to target a preferred natural frequency or frequencies is given in the conclusion.