This paper proposes a representation for the embodiment design of mechanical structures and a genetic algorithm suited for the representation. In order to represent early stages and latter stages of the embodiment design, the designs are modeled as simultaneous multi-objective optimization problems of parametric designs for parts and of layout generation for structures. The study, thus, involves genotypes that are adequate to represent phenotypes of the models for the genetic algorithm to solve the given problems. We demonstrate the implementation of the genetic algorithm with the result applied to the gear equipment design.