To palliate the hazards posed by satellites re-entering the atmosphere, international guidelines have defined a maximum acceptable risk for objects to re-enter uncontrolled. Containment methods attempt to reduce this casualty risk by maintaining critical components together such that the probability to collide with a human is reduced. In this thesis, four methods to contain objects are discussed: boxes, nets, tethers, and undemisable joints. Their advantages and disadvantages are preliminarily assessed, and the major caveats are identified. Two study cases are modelled and used to test the theoretical benefits of containment boxes and undemisable joints. Results suggest significant improvements, especially for optical payloads which typically lead to the uncontrolled re-entry scenario to be unacceptable. The critical dimensions and masses of several primitive shapes are also investigated for some of the most common materials used in space, in order to define thresholds for the containment net's maximum mesh size. Finally, the suitability of safety guidelines to rightly account for the hazards posed by containment compounds is addressed, and suggestions are provided to consider the kinetic energy of impactors to a higher extent.