The authors apply the ideal forming theory to design sheet stretching processes that can provide optimal shapes and optimal thickness distributions for flat sheets of uniform thickness. Specific design is developed for producing minimum weight shell structures that support a uniform pressure, assuming both von Mises and Tresca yield criteria together with rigid perfectly plastic flow condition. For the Tresca material, the optimum forming is hydraulic bulging of spherical shells. For the von Mises material, the optimum process is obtained numerically, and it is shown that the resulting process might be difficult to realise using conventional forming tools. However, the ideal forming information can provide useful guidance in the early stage of forming processes design.