Dealing with uncertainty adds a further level of complexity to problems of reliability analysis. The uncertainties which impact reliability studies usually involve incomplete or imprecise reliability data and complex failure dependencies. This paper proposes an original methodology based on the Transferable Belief Model (TBM) to include failure dependencies between components in the evaluation of the reliability of the whole system, given both epistemic and aleatory uncertainties. First, based on expert opinion and experimental data, Basic Probability Assignments (BPAs) are assigned to reliability data components. TBM operations are then used to obtain the reliability of the whole system, for series, parallel, series-parallel, parallel-series, and bridge configurations. Implicit, explicit, and discounting approaches are presented for taking account of failure dependencies. Finally, the proposed model is applied to take into account Common Cause Failures (CCFs) in a case study.