An elastomeric shock absorber having enhanced damping characteristics comprises a casing filled with a compressible elastomer; a piston rod immersed in the elastomer; a piston head mounted on the piston rod and the piston head is provided with connecting ports communicating with the front and back spaces of the piston and is also equipped with a mobile member. The mobile member is located between a surface from which the connecting ports emerge as well as a ring or like stop block. The stop block is mounted on a section of the piston head facing a flow chamber, wherein the piston head moves into and out of an outer cylindrical surface of the casing and wherein at least one groove is provided on an inner surface of the casing, which together with the outer cylindrical surface of the piston head form a flow chamber shaped as a solid of revolution, the solid of revolution being selected from the group comprising a cone, a ring, a torus and any combination thereof.