Over the past several decades increasing focus has been paid to the impact of structures where energy, during the impact event, needs to be absorbed in a controlled manner. This has led to considerable research being carried out on energy absorbers, devices designed to dissipate energy during an impact event and hence protect the structure under consideration. Energy absorbers have found common usage in applications such as vehicles, aircraft, highway barriers and at the base of lift shafts. A type of energy absorber which has received relatively limited attention in the open literature is the tapered rectangular tube. Such a structure is essentially a tube with a rectangular cross-section in which one or more of the sides are inclined to the tube's longitudinal axis. The aim of this thesis was to analyse the impact and energy absorption response of tapered and non-tapered (straight) rectangular tubes. The energy absorption response was quantified for both axial and oblique loading, representative of the loading conditions typically encountered in impact applications. Since energy absorbers are commonly used as components in energy absorbing systems, the response of such a system was analysed which contained either straight or tapered rectangular tubes as the energy absorbing components. This system could typically be used as the front bumper system of a vehicle. Detailed finite element models, validated using experiments and existing theoretical and numerical models, were used to assess the energy absorption response and deformation modes of straight and tapered tubes under the various loading conditions. The manner in which a thin-walled tube deforms is important since it governs its energy absorption response. The results show that the energy absorption response of straight and tapered rectangular tubes can be controlled using their various geometry parameters. In particular, the wall thickness, taper angle and the number of tapered sides can be effectively used as parameters to control the amount of absorbed energy. Tapered rectangular tubes display less sensitivity to inertia effects compared with straight rectangular tubes under impact loading. This is beneficial when the higher crush loads associated with inertia effects need to be reduced. Furthermore, though the energy absorption capacity of thin-walled rectangular tubes diminishes under oblique impact loading, the capacity is more maintained for tapered rectangular tubes compared with non-tapered rectangular tubes. Overall, the results highlight the advantages of using tapered rectangular tubes for absorbing impact energy under axial and oblique loading conditions. Understanding is gained as to how the geometry parameters of such structures can be used to control the absorbed energy. The thesis uses this knowledge to develop design guidelines for the use of straight and tapered rectangular tubes in energy absorbing systems such as for crashworthiness applications. Furthermore, the results highlight the importance of analysing thin-walled energy absorbers as part of an energy absorbing system, since the response of the absorbers may be different to when they are treated on their own.