The present paper describes the FEM code the present authors have developed based on the theory of the polycrystal plasticity with dislocation distributions taken into account and the simulations of tensile deformation behavior in FCC polycrystalline materials having bimodal structures by using the developed FEM code. In order to simulate the deformation behavior of materials having bimodal structures, it is necessary for the code to simulate the mesoscopic deformation behavior with the size effect of the initial yield strength, or the 0.2% proof strength. The present study has attempted to simulate the size effect of 0.2% proof strength by modifying the Bailey-Hirsch relation. By using the modified relation, the size effect of the initial plastic yield is successfully reproduced by FE polycrystal plasticity analysis. The results also showed that the 0.2% yield strength is decreased as the volume fraction of coarse grains is increased in the bimodal structure. As the ratio of the average diameter of fine grains to that of coarse grains is increased, the yield strength of the bimodal structure is decreased. The yield strength and work hardening rate of the bimodal structure, however, is not so much decreased as that of fine grain models. It was also revealed that the reason why materials having bimodal structures show higher ductility is that coarse grains yield in earlier stage of deformation and lower the maximum stress in the materials.