Both the SUPG/PSPG stabilized finite element method for the flow analysis and the enriched free mesh method (EFMM) for the solid analysis use the same type element, the linear triangle elements for 2D problems and the linear tetrahedral elements for 3D problems. Therefore, the handling of the fluid-structure interface becomes simple and accurate. On the other hand, the EFMM is not suitable for parallel computing because the domain decomposition is difficult for the EFMM data structure. In this study, we proposed the new approach for the parallelizing the EFMM and show some numerical examples of fluid-structure interaction problems. Furthermore, we proposed efficient asymmetric solver based on the Bi-CGSTAB method and GPBi-CG method.