This paper describes the deep geological repository concept considered by Nagra in support of its recent general licence application and the methodology used by Nagra to demonstrate its post-closure safety. The concept presented is for a deep geological repository for high-level waste (HLW) and for low- and intermediate-level waste (L/ILW) located in the Opalinus Clay host rock in Switzerland. The safety and repository concept is based on geological and engineered barriers which together perform a range of different high-level safety functions. The safety case is built on an assessment basis that is defined as the evidence, knowledge, assessment tools, and methodologies developed or acquired in support of the safety assessment. The safety assessment itself consists of four main steps or processes: i) performance assessment, in which arguments are developed and evidence presented to show that the safety functions of the repository are upheld and that the system will evolve as expected in most reasonably foreseeable situations, ii) safety scenario development, which defines a set of safety scenarios that capture alternative ways in which the repository system could evolve over time, taking uncertainty into account, iii) the analysis of radiological consequences, which uses quantitative models to evaluate annual individual dose rates or risks for these safety scenarios and compares the results with regulatory guidelines, and iv) the demonstration of post-closure safety, which synthesises the various lines of argument and evidence to produce the safety case. The paper provides an overview of the safety assessment methodology. Detailed aspects of performance assessment, safety scenarios development and the analysis of radiological consequences are provided in separate papers within this special issue.