Structure borne sound is one of the most important reasons of noise pollution in the automobiles and aircraft's. Noise is mostly generated by the vibrating panels excited by either a mechanical or an acoustical excitation. Examples of the typical vibrating structures in automobiles are engine cylinder, gearbox cover, transmission system covers, panels of the body etc. Sound radiation characteristics are also important in the phenomenon of resonant sound transmission through a panel. Resonant sound transmission occurs because of resonant modes of the panel within the frequency bandwidth of interest. Typical example of resonant sound transmission is the transmission through a firewall of an automobile, which forms the partition between the engine compartment and the cabin interior. Radiation characteristics can be typically defined by radiated sound power, radiation efficiency and space average mean square velocity of the panel. These radiation characteristics of the panels depend on the distribution of mass, stiffness and damping along the plate. Recent advances in composite technology have enabled the panel designs with complicated distribution of material properties. Design of such panels can be a challenging task since it involves a number of parameters. There can be a large number of feasible solutions with different values of parameters. Several optimization methods can be employed for finding an optimum set of variables which will give minimum value of the objective function.