A case study of the application of shape optimization technique to the design of the third cross-member of an automotive chassis has been presented. Its fundamental frequency is only marginally higher than the maximum operating frequency of the transmission and drive shaft, which are mounted on this cross-member. The objective is to raise the cross-member frequency as high as possible so that there is no resonance and resulting fatigue damage. A sizing optimization indicated that the mass was a predominant factor. Shape optimization using approximate direct linearization method was performed and a number of design directions were obtained. The fundamental frequency of the cross-member was raised by about 4 Hz.