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. Full scale structural testing of these processes is undertaken to verify the flexural and shear behaviours of non-prismatic elements. This is supported by further experimental and theoretical investigations into the durability of concrete cast in a permeable, flexible mould. Detailed analysis is provided alongside practical guidance for designers. Coupled with innovation in design and analysis techniques, flexible formwork is shown to provide a globally accessible method for the construction of low carbon, materially efficient and architecturally interesting concrete structures. Recognising the impact construction has on the environment, design philosophies centred around the need to put material where it is required are becoming increasingly desirable. This can now be achieved by replacing rigid formworks with systems comprised of flexible sheets of fabric. This is a step change in the way we think about our new concrete structures.