A damping and shock absorbing method and apparatus for permanent or non-permanent use in the human body consists out of a shape memory alloy material which is cycled through the stress-strain hysteresis to dissipate energy for an effective damping. A sufficiently high pre-stress is applied to the damping element(s) to ensure that the damping working range is within the superelastic cycle. The damping apparatus can be designed to work in tension or compression or - by combination of compression and tension elements - both in tension and compression. Moreover, damping elements from a shape memory alloy can be designed to work also in flexion and extension as well in rotation. The damping apparatus can be designed to have a stroke and force suitable for use in the human body by the design, the structure and the chemical composition of the shape memory alloy and their pre-set properties, such as plateau stresses of the superelastic cycle depend on the ambient temperature, the force of damping elements can also be changed in-situ by changing the temperature of the damping elements. The damping elements out of a shape memory alloy can be combined with elastic elements out of other materials to achieve stress- strain behaviour more suitable for use in the individual human body.