Construction of concrete shells is expensive and generates wastes from the fabrication of formworks. Being non-reusable, these elements have a negative impact on the life-cycle assessment of the construction. The purpose of this research is to design and build a new inexpensive formwork system made of inflatable structures for precast and thin concrete shells construction. By sealing two membranes according to a pattern, this system allows the construction of complex inflated shapes. The sealing pattern is designed such that, once inflated, the planar metric becomes not uniform and generates a 3D surface following Gauss's Theorema Egregium, a classical result of differential geometry. This design of the seal pattern is guided by a numerical tool capable of accurately predicting the inflated shape. The simulations are compared to physical models made of fabrics, before manufacturing inflatable formwork prototypes in composite membranes from about 1 to three metres wide. Support is set up to pour concrete on the inflatable formwork without damaging it for reuse. The resulting thin concrete shell and its fabrication method are eligible for wider-scale application in the AEC industry.