The invention belongs to the field of an elastic damping supporting structure, and in particular relates to a slender rod type low-rigidity elastic damping supporting structure. A supporting base is arranged at the bottom in an elastic damping supporting base cavity, the center of the supporting base is provided with a hole and a slender rod elastic support is arranged in the hole; a damping body is a hollow sleeve, is sheathed on the slender rod elastic support and is fixedly connected with the slender rod elastic support; the top part of the damping body is provided with a bearing base, and the top part of the slender rod elastic support is inserted into the bearing base; the center of the top part of the bearing base is provided with a bearing which is internally provided with a pivot; and lubricating oil is filled in an elastic damping supporting base and immerses the bearing. When designed and applied to an energy-storage fly wheel, the slender rod type low-rigidity elastic damping supporting structure can be used as the elastic damping support with long life and high reliability; when applied a high-speed centrifuge, the slender rod type low-rigidity elastic damping supporting structure is capable of reducing the manufacturing cost of the elastic support; and when the slender rod type low-rigidity elastic damping supporting structure is applied to isotope separation machinery, great economic benefit is generated due to scale effect.