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Composite manufacturing demands mould tooling to produce dimensionally accurate parts, adding substantial capital costs to their production. Recent developments in advanced manufacturing of fibre-reinforced polymer composite elements have seen the implementation of mould-free technologies that can produce complex shaped parts off a flat tool. This paper presents eccentric fibre prestress as a novel mould-free method for producing curvatures within carbon fibre and glass fibre laminates. Tailoring the flexural rigidity along the primary orientation of the laminate is shown to result in predictable compound curvature profiles with a low average root mean square error of 1.39 across the four geometries tested. An analytical model based on Euler–Bernoulli beam theory is proposed and proven to correlate closely with the experiential laminates. Finally, an inverse design approach based on a genetic algorithm is demonstrated to design an accurate laminate configuration, achieving the top surface of a NACA 4412 aerofoil section with a low root mean square error of 1.98 using the proposed eccentric fibre prestress. [ABSTRACT FROM AUTHOR]