This paper focuses on the behaviour of pressurised thick-walled cylinder made of incompressible isotropic nonlinearly elastic material. The study aims to analyse the behaviour and stress field of such material, which is characterised by high deformability. An analytical solution is proposed for the general form of the free strain energy function. Six different types of strain energy functions are applied to a pressurised thick-walled hollow cylinder to model the material behaviour. A closed-form analytical solution is obtained for this problem and the results predicted from classic strain energy models (neo-Hookean and Mooney–Rivlin) and those obtained by Gent, Isihara and Ogden models are compared in the prescribed case. These comparisons are done to investigate the accuracy and evaluating effectiveness of some existing constitutive models in the analysis of cylindrical vessel under pressure. Some designing factors including axial stretch and radius ratio are studied.