This paper presents a pioneering effort to ascertain the suitability of hyperelastic modelling in simulating the stress–strain response of oil palm shell reinforced rubber (ROPS) composites. ROPS composites with different oil palm shell contents (0%, 5%, 10% and 20% by volume) were cast in the laboratory for the experimental investigation. ROPS specimens with circular, square, hexagon, and octagon shapes (loading surface) were considered to evaluate the accuracy of finite element simulation considering the shape effect of composites. Strain-controlled (compressive) tests with ε ≈ 50% at 0.8 Hz frequency were conducted in the laboratory and the test data obtained was used as input to simulate material coefficients corresponding to the strain energy functions chosen. Five different strain energy functions were selected and utilized for the hyperelastic modelling in this study using finite element approach. The shape effect was then used to ascertain any variation in the simulation outcomes and to discuss the effect of shape on the behaviour of ROPS composites in comparison to existing literature. The numerical predictions using the Yeoh model (error ≤ 2.7% for circular shaped ROPS) were found to perform best in comparison with the experimental results, thus a more stable and suitable hyperelastic model to this end. The Marlow (error ≤ 4.6% for circular shaped ROPS) and Arruda Boyce (error ≤ 4.7% for circular shaped ROPS) models were amongst the next alternatives to perform better. Even with the other shapes considered in this study, Yeoh, followed by the Marlow function, were more appropriate models. The shape effect was then studied with particular emphasis on comparing and assessing them with that observed in the literature. To this end, adopting the Yeoh function in the finite element model is the ideal approach to estimate the stress–strain response of ROPS composites.