Over the last few decades, a number of major industrial blast accidents involving oil and gas installations occurred worldwide. These include the blast explosion that occurred in an industrial facility at Buncefield in the United Kingdom in 2005. Extensive damage occurred due to the blast, both to the industrial plant and surrounding buildings, as a consequence of much higher overpressures than would normally be expected from a vapour cloud explosion of this nature. In response to this event, a great deal of work was carried out on collecting and analysing available evidence from the incident in order to understand the explosion mechanism and estimate the overpressure levels within the gas cloud that formed. Subsequent investigations included the examination of steel switch boxes on the site located within the area covered by the vapour cloud. These boxes suffered varying degrees of damage and could therefore be used as overpressure indicators. A series of tests were commissioned after the event in order to compare the damage of the field boxes with detonation tests on similar boxes. The thesis firstly reports on numerical studies carried out on assessing the damage to steel boxes subjected to both detonation and deflagration scenarios in order to aid the investigation of the explosion. Several modelling approaches are adopted in the numerical studies, including: Pure Lagrangian, Uncoupled Lagrangian-Eulerian and Coupled Lagrangian-Eulerian techniques. The numerical models are validated against data collected from gas detonation experiments on similar steel boxes. It is found that the coupled approach is able to predict the results accurately, although such an approach cannot be used in detailed parametric investigations due to its prohibitive computational demand. The pure Lagrangian approach is therefore used instead, but the overpressure range in the parametric assessments is limited to 4 bar (side-on) as an adequate level of accuracy from this modelling technique cannot be ensured beyond this range. The results are summarised in the form of pressure-impulse diagrams, and typical residual shapes are selected with the aim of aiding forensic investigations of future explosion incidents. The investigation is extended thereafter to the response of a steel-clad portal frame structures located outside the gas cloud and which suffered varying degrees of damage. A typical warehouse building is studied through a pure Lagrangian approach. A non-linear finite element model of a representative sub-structure of the warehouse wall is validated against a full scale test carried out at Imperial College London. A series of pressure-impulse diagrams of the sub-structure is then constructed based on the results of parametric non-linear dynamic assessments using the developed numerical model under various combinations of overpressures and impulses. A new failure criterion based on the total failure of the self-tapping screws is proposed in conjunction with pressure-impulse diagrams. This failure condition provides a more direct assessment of the damage to the side walls of the warehouse. The pressure-impulse diagrams can be used to assess the response of a typical warehouse structure to blast loading, and to provide some guidance on the safe siting in a hazardous environment around oil and storage sites. Simplified approaches based on single degree of freedom representations are also employed, and their results are compared with those from the detailed non-linear finite element models. The findings show that the simplified approaches offer a reasonably reliable and practical tool for predicting the response of the side rails. However, it is illustrated that such idealisations are not suited for assessing the ultimate response of cladding panels, as the side rail-cladding interactions cannot be captured by simplified approaches and necessitate the deployment of detailed numerical procedures.