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A computationally efficient framework is presented to design fibre steered laminates in cylindrical shells, stiffened with longitudinal stiffeners, optimally. The framework is comprised of a semi-analytical analysis approach and a multi-step optimisation framework, and is applied for maximum buckling capacity design of fibre steered laminates of two stiffened cylinders, with different thickness to radius ratios, under bending moment. If the maximum buckling capacity designs are material failure critical, strength is imposed as a constraint in the optimisation problem. Comparisons of buckling capacity of steered fibre laminates with those of straight fibre laminates are shown and validated. Finally, to gain in-depth understanding of the way buckling capacity is improved by fibre steering, the axial section load and the critical buckling modes of straight and steered fibre laminates are compared. [ABSTRACT FROM AUTHOR]