The mechanical response of pressure vessels to an applied internal pressure is essentially controlled by a few key parameters, related both to the overall geometry of the structure and to the orientations and thicknesses of the composite layers. The role of each parameter, and the way they interact to determine the structural response, can be apprehended at a very early design stage by using simple material and structural models, which enable to explore a wide range of designs with minimal computational cost. More complex models can then be called into play to predict the detailed structural response, including crucial information such as the burst pressure and failure mode. This paper discusses a hierarchy of models with increasing levels of details and complexity, which are useful to gain increasing insight on the pressure vessel response all along the design process.