This paper presents a model to predict the shear resistance of the unreinforced lightweight concrete core of a recently developed hybrid sandwich concept for bridge decks. The sandwich skins consist of a fiber-reinforced polymer (FRP) composite sheet for the tensile skin and a thin layer of high-strength concrete as a compression skin. The model uses a fracture mechanics approach and considers the shear force transmitted in the fracture process zone where a tensile load transmission through an initiating crack is still possible. To verify the modeling results, experiments on 12 sandwich beams were carried out. In contrast to the Eurocode 2 model for shear resistance prediction, the proposed model demonstrated a good agreement to experimental results and highlighted the importance of considering not only the static strength, but also fracture mechanics properties such as the characteristic length.