[Truncated abstract] The analysis and subsequent interpretation of trace evidence is of paramount importance to the forensic scientist. While a variety of methods are available to facilitate comparison between recovered and control samples, the use of a specific analytical method depends upon both the physical and chemical nature of the material itself and the material to which it is to be compared. Elemental analysis of evidentiary material is one such method of sample comparison and has been extensively applied to this purpose following the introduction of neutron activation analysis in the early 1960s. However, over the last 15 years, another instrumental technique has taken centre stage in the analytical armoury of the forensic scientist: laser ablation–inductively coupled plasma-mass spectrometry (LA-ICP-MS). The modification and adaptation of this technique, to a point where it is possible to distinguish between glass materials produced only hours apart on the same production line, is detailed in this thesis. Additional protocols have also been developed for the analysis of fibreglass and plastic crime scene debris. Finally, a method for quantification of elemental concentrations in headlamp plastics has also been developed to facilitate inter-comparison of data between both different analytical techniques and different laboratories. Glass material is one of the most common varieties of trace evidence and the forensic examination of glass traditionally involves the determination of its refractive index (RI). ... The analytical protocol involves the analysis of 46 analytes on material comprising the exterior surface of the lens. Using this data, it was found that although minor variations in elemental composition exist within a single headlamp lens, discrimination between lenses produced from a single manufacturing plant over a short period of time could still be achieved. Discrimination between all headlamp lenses, with the exception of some lenses produced on the same day, could be facilitated using the analytical protocol developed. Furthermore, an interpretational protocol has been developed that has successfully classified all unknown headlamp lens samples investigated in this study, within the discrimination limits of the analytical method. The semi-quantitative analysis of glass and plastic samples has also been examined using LA-ICP-MS. The concentrations of 16 analytes in container and float glass samples were determined. However, the levels of discrimination afforded by the semi-quantitative data were inferior to those achieved using qualitative data. Finally, a series of plastic-based standards, containing 25 analytes of known concentrations, was produced. Using these standards, relative concentrations of the study analytes were determined in polycarbonate headlamp lenses. Interpretation of the data produced made it possible to discriminate between all study samples. Consequently, the total analytical and interpretational protocol developed in this study has established the foundation for LA-ICP-MS to be adopted internationally as a recognised method for the analysis of plastic crime scene debris.