In this work, a method for the application of multi-fidelity modelling to the reliability analysis of 2D elastostatic structures using the Boundary Element Method (BEM) is proposed. Reliability analyses were carried out on a rectangular plate with a centre circular hole subjected to uniaxial tension using Monte Carlo Simulations (MCS), the First Order Reliability Method (FORM), and the Second Order Reliability Method (SORM). Two BEM models were investigated, a low-fidelity model (LFM) of 20 elements and a high-fidelity model (HFM) of 100 elements. The response of these models at several design points was used to create multi-fidelity models (MFMs) utilising 2nd order polynomial response surfaces and their reliability, alongside that of the LFM and the HFM, was evaluated. Results show that the MFMs that directly called the LFM were significantly superior in terms of accuracy to the LFM, achieving very similar levels of accuracy to the HFM, while also being of similar computational cost to the LFM. These direct MFMs were found to provide good substitutes for the HFM for MCS, FORM, and SORM.