This paper presents a design method to optimize the material distribution of functionally graded beams with respect to some vibration and acoustic properties. The change of the material distribution through the beam length alters the stiffness and the mass of the beam. This can be used to alter a specific beam natural frequency. It can also be used to reduce the sound power radiated from the vibrating beam. Two novel volume fraction laws are used to describe the material volume distributions through the length of the FGM beam. The proposed method couples the finite element method (for the modal and harmonic analysis), Lumped Parameter Model (for calculating the power of sound radiation), and an optimization technique based on Genetic Algorithm. As a demonstration of this technique, the optimization procedure is applied to maximize the fundamental frequency of FGM cantilever and clamped beams and to minimize the sound radiation from vibrating clamped FGM beam at a specific frequency.