This paper presents a preliminary framework to inform the analysis and design of tangible narratives. Researchers and designers have been using tangible user interfaces (TUIs) for storytelling over the past two decades, but to date no comprehensive analysis of these systems exists. We argue that storytelling systems that use digitally-enhanced physical objects form a unique medium with identifiable narrative characteristics. Our framework isolates these characteristics and focuses on the user's perspective to identify commonalities between existing systems, as well as gaps that can be addressed by new systems. We find that the majority of systems in our sample require the user to perform exploratory actions from an external narrative position. We note that systems that cast the user in other interactive roles are rare but technologically feasible, suggesting that there are many underexplored possibilities for tangible storytelling.