In the late 1960s, Hans-Jörg Schek, a mathematician, developed the Force Density Method, a mathematical method to design shell structures consisting of various materials such as fabric, cable nets, or concrete. Starting from a curve fitting ansatz he developed a method whereby a global parameter (force density) would control the shape of a self-supporting structure. Linearising the resulting equations, the solutions could be computed by the computers available in those days. This case study demonstrates how mathematical insights where used to overcome the limitations of the computing technology at hand in the application area of architecture and civil engineering around 1970. Firstly, we provide the context of conducting calculations using curve and surface fitting or the Finite Element Method in architecture and civil engineering. In a second step, the manner is studied in which these algorithms were transformed into software. The structure of the software packages is examined and their further developments will be traced. Finally, it is shown how the new algorithms contributed to the design of the membrane roof of the 1972 Olympic Stadium in Munich.