The shape and topology optimization method using a homogenization method is a powerful design tool because it can treat topological changes of a design domain. This method was originally developed in 1988  and have been studied by many researchers. However, their scope of application in real vehicle design works has been limited where a design domain and boundary conditions are very complicated. The authors have developed a powerful optimization system by adopting a general purpose finite element analysis code. A method for treating vibration problems is also discussed. A new objective function corresponding to a multi-eigenvalue optimization problem is suggested. An improved optimization algorithm is then applied to solve the problem. Applications of the optimization system to design the body and the parts of a solar car are presented. An example of multi-eigenvalue optimization problems is also shown to optimize several eigenfrequencies of a simplified model of a car body simultaneously.