The conceptual design of a helical fusion reactor was studied at the National Institute for Fusion Science in collaboration with other universities. Two types of the force free helical reactor (FFHR) are FFHR-d1 and FFHR-c1. FFHR-d1 is a self-ignition demonstration reactor that operates with a major radius of 15.6 m at a magnetic field intensity of 4.7 T. FFHR-c1 is a compact subignition reactor that aims to realize steady electrical self-sufficiency. Compared to FFHR-d1, FFHR-c1 has a magnetic field intensity of 7.3 T and a geometrical scale of 0.7. The location of the superconducting coils in both types of FFHR is based on that of the Large Helical Device (LHD). LHD has a major radius of 3.9 m. According to the design of LHD, the deformation must be within the required value to compensate for the accuracy of the magnetic field. According to this concept, the magnet support structure of LHD was fabricated using thick Type 316 stainless steel to impart sufficient rigidity. Thus, the stress of the magnet system of LHD is sufficiently below the permissible stress. In the case of FFHR, from the viewpoint of the reactor, a large access port is required for the maintenance of the in-vessel components. The mechanical design of the support structure is conceptualized by considering the basic thickness of the material and residual aperture space by referencing the mechanical analysis results. Details of the design concepts of LHD and FFHR-d1/FFHR-c1 as well as the results of mechanical analyses are introduced in this paper.