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Every engineering parameter has uncertainty in its value. However, taking this into account when analysing the reliability or the remaining life of engineering structures can be computationally expensive. This is especially true for aircraft structures, which can have complex geometries and loading conditions. To improve the efficiency of these analyses and therefore enable them to be more readily applied to more complex structures, novel Boundary Element Method (BEM) formulations have been developed for the first time and are presented in this thesis. These formulations enable the safety of complex structures to be more readily determined; potentially improving safety, reducing weight, fuel consumption, and carbon emissions from aviation. To further improve efficiency, new metamodelling-based formulations with the BEM, making use of techniques such as Kriging and multi-fidelity modelling, have been developed. Based on the results of several numerical examples, including aircraft stiffened panels, the developed formulations proved very effective when used with reliability analysis methods such as Monte Carlo Simulation (MCS), the First-Order Reliability Method (FORM), and the Second-Order Reliability Method (SORM), as well as with life analysis methods such as the Equivalent Initial Flaw Size (EIFS) method. The newly developed BEM formulations for reliability analysis required 3-5 times less runtime than existing methods while demonstrating very small differences in accuracy of only 1-3\%. In addition, EIFS was determined within only 10\% error using the data from only 50 simulated inspections. The use of metamodelling was also very effective. The metamodels were up to 61,000 times faster than the BEM models used to train them but provided levels of error typically much less than 1\%. Results suggest that these newly developed BEM formulations have the capability to efficiently analyse, with confidence and in the presence of significant operational and manufacturing uncertainties, the reliability and remaining life of complex engineering structures.