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Steel pipelines play an important role in the oil and gas industry. Hence, corrosion of the steel pipe systems during its service life is a critical issue for the industry. Fibre-reinforced composites offer solutions with broad applicability and efficiency for the internal repair of these corroded pipelines. Understanding the behaviour of internal composite repair systems against different internal pressure regimes is an important aspect in the development of a repair system. This study develops the analyses of internal composite bonded repair systems for long steel pipes with an axisymmetric defect, based on Lame’s equation. Various levels of bonding between the steel and composite are studied. Fully bonded optimum internal composite repair thicknesses are determined using biaxial carbon and glass fibre composites for different levels of corrosions, using the von Mises yielding and Tsai–Hill failure criterion approaches. Two case studies are illustrated using the design nomographs. The analysis technique used was found to be accurate when compared with finite element modelling results. [ABSTRACT FROM AUTHOR]