Metastable failure is a recent abstraction of a pattern of failures that occurs frequently in real-world distributed storage systems. In this paper, we propose a formal analysis and modeling of metastable failures in replicated storage systems. We focus on a foundational problem in distributed systems -- the problem of consensus -- to have an impact on a large class of systems. Our main contribution is the development of a queuing-based analytical model, MSF-Model, that can be used to characterize and predict metastable failures. MSF-Model integrates novel modeling concepts that allow modeling metastable failures which was interactable to model prior to our work. We also perform real experiments to reproduce and validate our model. Our real experiments show that MSF-Model predicts metastable failures with high accuracy by comparing the real experiment with the predictions from the queuing-based model.