Safety arguments, also called safety cases, are commonly used to demonstrate that adequate efforts have been made to achieve safety goals. Assessing the confidence of such arguments and decision-making is usually done manually and is heavily dependent on subjective expertise. Therefore, there is an urgent need for an approach that can assess confidence in the arguments in order to support decision-making. We therefore propose a quantitative approach, based on Dempster-Shafer (D-S) theory, to formalize and propagate confidence in safety cases. Goal Structuring Notation is adopted. The proposed approach focuses on the following issues regarding argu-mentation assessment: 1) formal definitions of confidence measures based on belief functions from D-S theory; and 2) the development of confidence aggregation rules for structured safety arguments with the help of Dempster's rule. Definitions of confidence measures and aggregation rules are deduced for single, double, and n-node arguments. Finally, a sensitivity analysis of aggregation rules is used to preliminarily validate this approach.