In the context of critical applications, such as shielding and radiation protection, ensuring the quality of simulation software they depend on is of utmost importance. The assessment of simulation software quality is important not only to determine its adoption in experimental applications, but also to guarantee reproducibility of outcome over time. In this study, we present initial results from an ongoing analysis of Geant4 code based on established software metrics. The analysis evaluates the current status of the code to quantify its characteristics with respect to documented quality standards; further assessments concern evolutions over a series of release distributions. We describe the selected metrics that quantify software attributes ranging from code complexity to maintainability, and highlight what metrics are most effective at evaluating radiation transport software quality. The quantitative assessment of the software is initially focused on a set of Geant4 packages, which play a key role in a wide range of experimental applications and are representative of different software development processes. We provide an interpretation of the data resulting from measurements on the selected Geant4 packages, and discuss methods to improve them. This work can be used as a baseline for evaluating correlations between software quality embedded in the Geant4 development process and simulation observables produced by Geant4-based applications. The result provide constructive guidance both to improve key software tools, such as Geant4, and to estimate their contribution in risk analyses concerning sensitive applications.