Damping elements for tool chucking systems for damping vibrations and shocks that occur during machining in the case of force-fitting clamping of tools in a tool receptacle or on the tool itself. At least one damping element consisting of a shape memory alloy having a mechanical effect is provided in a tool chucking system or on the tool itself, such that the damping element provided in the chucked state in the force flow of the chucked elements is present in a reversible and hysteresis-dependent state by way of a mechanical force action and the associated crystalline conversion via the pretensioning of said damping element and leads to dissipation of mechanical energy. The mechanical energy to be damped is a cyclical vibration or represents a non-cyclical overload which is transmitted in the form of shocks.