Risk-based design of marine pressure hulls require computationally efficient and precise models predicting collapse pressures of ring stiffened cylindrical shells as a function of realistic geometrical imperfections. However, the empirical interframe collapse models commonly implemented in design codes do not explicitly depend on imperfections, and the existing analytical models are only valid for axisymmetrically imperfect shells. The goal is to derive an analytical model that explicitly depends on axisymmetric and asymmetric imperfections. In order to derive such a model, first the stress development is investigated using the nonlinear Finite Element Analysis (FEA) of twelve marine pressure hulls having axisymmetric imperfections only. The knowledge gained from these investigations is used to qualify three collapse models. One of them, the integral model introduced by the authors, is accurate and sufficiently precise. It uses a new definition of interframe collapse, which also allows for asymmetric imperfections.