A combined method of a genetic algorithm and finite element stress analysis has been developed to design the structure of materials. The genetic algorithm is applied to searching structures that have a desired property by combining it with the finite element analysis, which is used to predict the elastic modulus and Poisson's ratio. The calculation of the stress analysis is validated from the comparison with the theory on parallel, series, and random structures. The combined method was applied to two searches of structures. One was to find structures that have a desired elastic modulus, respectively. The calculation successfully found a proper structure for each desired elastic modulus. The other was the search of the structure that shows a negative Poisson's ratio. A structure having the negative Poisson's ratio was generated by the calculation. Although this original structure would appear to have no features, it gave us a good idea for the design of materials by investigating the stress distribution in the original structure. A new structure that consists of a unique and continuous pattern of the higher elastic component was designed from the calculation. The reason for the negative Poisson's ratio is explained by mechanical linkage.