Concrete, our most widely used construction material, is a fluid that offers the opportunity to economically create structures of almost any geometry. Yet this unique fluidity is seldom capitalised on, with concrete instead being cast into rigid prismatic moulds to create high material use structures with large carbon footprints. Our rate of concrete consumption means that cement manufacture alone is estimated to account for some 5% of global Carbon Dioxide emissions. This dissertation shows that by replacing conventional orthogonal moulds with a flexible system comprised primarily of high strength, low cost fabric sheets, the fluidity of concrete can be utilised to create structurally optimised concrete structures. Flexible formwork therefore has the potential to facilitate the change in design and construction philosophy that will be required for a move towards a less material intensive, more sustainable, construction industry. Optimisation and design processes developed in this thesis show that material savings of up to 40% are possible in flexibly formed concrete beams.