Advanced biliary tract cancer (BTC) has a poor prognosis and limited treatment options. The PI3K/Akt/mTOR signalling pathway is hyperactivated in a subset of BTCs, and clinical activity of the mTOR inhibitor everolimus has been observed in some patients with BTC. The goal of this study was to identify biomarkers predictive of everolimus response. Twenty BTC cell lines were assessed for everolimus sensitivity with a spectrum of growth inhibitory responses observed. Molecular biomarkers of sensitivity and resistance were identified by interrogation of the activation status of the Ras/MAPK and PI3K/Akt/mTOR pathways. K‐Ras mutations and/or amplifications were identified in 45% of cell lines and were associated with resistance to everolimus. Activating mutations in PIK3CA or loss of PTEN was not predictive of everolimus response; however, high basal levels of pAKT were associated with sensitivity, independent of Ras/MAPK pathway activation status. Notably, everolimus inhibited mTOR signalling to a similar extent in sensitive and resistant cell lines, suggesting that relative dependence on the mTOR pathway rather than the magnitude of pathway inhibition determines everolimus response. Consistent with the known limitations of rapalogs, everolimus induced feedback‐mediated activation of AKT in BTC cell lines, which could be overcome by cotreatment with an AKT inhibitor or ATP‐competitive mTORC1/mTORC2 inhibitors. However, both approaches failed to induce greater apoptosis compared to everolimus, and mTORC1/mTORC2 kinase inhibitors induced compensatory activation of pERK, identifying an inherent limitation of these agents in BTC cell lines. These findings suggest that future trials of everolimus in BTC would benefit from preselecting patients based on their K‐Ras and PI3K/mTOR pathway activation status. The study also identifies strategies for enhancing inhibition of the PI3K/mTOR pathway in BTC cell lines.