Facing the challenges of our environmental crisis, the AEC sector must significantly lower its carbon footprint and use of first-use resources. A specific target is the reduction of the amount of concrete used. Funicular structures that base their strength on their structurally-informed geometry allow for material efficiency. However, a bottleneck for their construction lies in their costly and wasteful formworks and complex reinforcement placement. This research presents an alternative flexible formwork system consisting of a bending-active gridshell falsework and fabric shuttering for ribbed funicular concrete shells. The falsework becomes structurally integrated as reinforcement and is designed as two connected layers offering shape control and sufficient stiffness to support the wet-concrete load. The paper focuses on the development of a design-to-fabrication workflow and a graph-based data structure for gridshell falsework and reinforcement in the computational framework COMPAS. The implementation utilises, customises and creates packages for the form finding of the ribbed shell with TNA and the gridshell with FEA. The research is based on a demonstrator realised in the context of the Technoscape exhibition at the Maxxi Museum in Rome, Italy. The computational workflow was used to design this system and translate it for materialisation. The demonstrator serves as proof-of-concept for the novel material-efficient construction system. Its key to efficiency lies in the structurally-informed geometry for both the formwork and the resulting ribbed concrete shell.