The invention relates to a cylindrical tension and compression support for transferring an upper load to a lower part or pier foundation. The cylindrical tension and compression support comprises an upper support skirt part and a lower support skirt part which are respectively provided with bolt holes connected with a main body structure, wherein the upper part of the upper support skirt part is in a rectangular or circular shape, and the lower part of the upper support skirt part is in an incomplete cylindrical shape; the incomplete cylinder is connected with the arc of the upper part of the upper support skirt part, and the middle of the lower support skirt part is provided with a cylindrical surface groove for the incomplete cylinder to freely rotate or transversely slide; local reinforcing ribs are arranged on the lower support skirt part. During installation, the incomplete cylinder is pushed into the cylindrical surface groove from the side, and the groove can bear the vertical pressure and also transfer the vertical pull due to the narrow upper part and the wide lower part of the groove. The cylindrical tension and compression support provided by the invention is simple in structure, is used for a fulcrum needing to transfer the pull and pressure, and is applied to large rotation and horizontal displacement of the structure, the bending internal force at a beam end is avoided, the structural design is simplified, and the manufacturing cost is reduced.