The design and manufacturing of concrete elements need to be reconsidered in light of current trends in architectural geometry. Today, there is a movement toward greater customization and adaptability of concrete elements using “reconfigurable formworks” and “additive manufacturing.” Our study approached the issue of fabricating non-standardized concrete elements from the perspective of a “reconfigurable fabrication platform.” Specifically, we developed a method of fabricating geometrically diverse concrete joints by combining flexible pressure-enduring tubes with a rigid mechanism, resulting in an adaptive concrete-casting machine. This platform, which we named “Flexi-node,” can be used in conjunction with a relevant fabrication-aware digital design tool. Users can computationally design and fabricate a great variety of concrete joints using just one mold, with a minimum of material waste and with no distortion from hydrostatic pressure as would typically occur in a fully flexible formwork.