This study presents a novel computational model to investigate the bending behaviour of thin- and thick-walled composite pipes made from fully bonded fibre-reinforced thermoplastic composite materials. The primary objective is to analyse the stress state and predict potential failure modes of these pipes, which have gained significant interest in the oil and gas industry due to their advantageous properties. The developed model is validated through comparisons with finite element analysis and published results, demonstrating its accuracy and adaptability. Utilising the validated computational model, safety zones for composite pipes with various stacking sequences are established, providing valuable insights into the optimal design of composite pipes under bending loads. Furthermore, the method is employed to determine the maximum bending moment and critical bendable radius of the pipe, revealing the direct correlation between maximum bending moment and bending stiffness, independent of the bending radius. The findings of this study offer practical guidance for the design and optimisation of composite pipes in the oil and gas industry, promoting their adoption as a viable alternative to traditional metal pipes. The developed computational model serves as an efficient and reliable tool for engineers to make informed decisions in the design and selection of advanced composite materials for pipe applications, enabling the optimisation of pipe performance under various bending load scenarios.