The material requirements for present industries have led researchers to look for materials with high specific strength, stiffness and eco-friendliness. Research studies on natural-fibre-reinforced polymer matrix composite materials have increased to satisfy industry requirements. Reinforcement enhances the rigidness of composite materials, which is measured through shear modulus values. This work attempted to use carbon nanotube (CNT)/coir fibre/fly ash as reinforcements with epoxy. The experimental specimens were made by varying the contents of CNT/coir fibre/fly ashwith epoxy by using the response surface methodology, one of design-of-experiment approaches. Analysis of variance was used to study the influence of the reinforcement percentage of CNT/coir fibre/fly ash on the shear modulus of the composite. Two models were obtained to predict the shear modulus for various reinforcement parameters using the experimental data. This was based on the regression equation meant for shear modulus. Of the two models, one was based on an artificial neural network and other was based on a multiple linear regression model. Optimum reinforcement parameters were obtained through a teaching-learning-based optimisation algorithm. A confirmation test was also carried out to determine the shear modulus experimentally for the reinforcement parameters obtained from the optimisation process. © 2020 ICE Publishing. All rights reserved.