Conventional formworks for concrete curved shells either are expensive, complex and wasteful or have formal restrictions. Using tile vaults (also known as timbrel, Guastavino, thin-tile or Catalan vaults) as stay-in-place formwork for concrete shells could significantly reduce construction costs and material waste. Tile vaults only require formwork at the boundaries and provide a high formal flexibility. The combination of masonry and reinforced concrete creates a new type of composite structure that needs experimental validation and new structural analysis models to deal with the specific features of the system. This paper presents experimental research on the component materials, load tests on doubly-curved, full-scale prototypes and the definition of a reliable Finite Element structural model for the analysis of the proposed hybrid structure. The experimental research has involved the characterisation of the bricks, mortar, concrete and reinforcement composing the proposed system in order to provide the material properties to be considered in the structural analysis. The construction and testing of two composite sail domes in the laboratory have allowed the validation of the proposed FE model by comparing its predictions with the collapse mechanisms, damage, ultimate loads and load–displacement curves obtained experimentally.