The invention discloses an anti-buckling support with circumferential prestressing, a method and application. The anti-buckling support comprises a support core material, an inner sleeve and an outer sleeve, wherein a steel pipe is used as the core material; the inner sleeve is used for supplying circumferential prestressing to the core material and is arranged in the support core material; the outer sleeve is used for improving the local stable bearing capacity and overall stable bearing capacity of the support core material and is arranged outside the support core material; and a friction reducing layer is respectively arranged between the support core material and the inner sleeve as well as between the support core material and the outer sleeve so as to reduce the limit of the inner and outer sleeves to axial deformation of the core material. According to the anti-buckling support, the self weight of the support is small, and although the cross section of the structure is composed of three layers of steel pipes, the combined section is still a hollow section; compared with a solid section, the component weight is greatly reduced, and the hysteretic behavior is good; the support core material, the outer sleeve and the inner sleeve are made of uniform steel products, so that the strength is high, the durability is good, and the hysteretic behavior is good; and the circumferential prestressing is applied to the core material so as to reduce the axial bearing capacity of the core material, so that the core material is easier and faster to yield, the shock resistance is improved, and the energy consumption is reduced.