The invention belongs to a shock absorbing technology and relates to a tensile compression-resistant high-rigidity cylindrical shock absorber. The tensile compression-resistant high-rigidity cylindrical shock absorber comprises a shell (1) as well as an outer cylinder (2), an inner cylinder (3) and a rubber elastomer (4) which are mounted on the shell (1), and is characterized in that a pluralityof fan-shaped reinforcement rib plates are uniformly arranged on the outer side of the inner cylinder (3) and the inner side of the outer cylinder (2); the inner cylinder (3) and the outer cylinder (2) are connected through the filling with the rubber elastomer (4); and the fan-shaped reinforcement rib plates are embedded in the rubber elastomer (4). The tensile compression-resistant high-rigiditycylindrical shock absorber provided by the invention has the characteristics that the axial rigidity is high; the rigidity designability is high; the limiting protection of tension and compression isachieved; the structure is simple; the use and the maintenance are convenient; and the cost is low.