This paper presents an original method for evaluating reliability indices for Multi-State Systems (MSSs) in the presence of aleatory and epistemic uncertainties. In many real world MSSs an insufficiency of data makes it difficult to estimate precise values for component state probabilities. The proposed approach applies the Transferable Belief Model (TBM) interpretation of the Dempster-Shafer theory to represent component state beliefs and to evaluate the MSS reliability indices. We use the example of an oil transmission system to demonstrate the proposed approach and we compare it with the Universal Generating Function method. The value of the Dempster-Shafer theory lies in its ability to use several combination rules in order to evaluate reliability indices for MSSs that depend on the reliability of the experts' opinions as well as their independence.