Metaphors are a powerful conceptual device to reason about human actions. As such, they have been heavily used in designing and describing human computer interaction. Since they can address scripted text, verbal expression, imaging, sound, and gestures, they can also be considered in the design and analysis of multimodal interfaces. In this paper we discuss the description and evaluation of the relations between metaphors and their implementation in human computer interaction with a focus on tangible user interfaces (TUIs), a form of multimodal interface. The objective of this paper is to define how metaphors appear in a tangible context in order to support their evaluation. Relying on matching entities and operations between the domain of interaction and the domain of the digital application, we propose a conceptual framework based on three components: a structured representation of the mappings holding between the metaphor source, the metaphor target, the interface and the digital system; a conceptual model for describing metaphorical TUIs; three relevant properties, coherence, coverage and compliance, which define at what extent the implementation of a metaphorical tangible interface matches the metaphor. The conceptual framework is then validated and applied on a tangible prototype in an educational application.