In this work, nonwoven kenaf fibre/epoxy composites were produced by using resin transfer moulding. The effect of kenaf fibre volume fraction on the composites’ tensile properties and Poisson’s ratio was investigated. Experimental results show that highest tensile properties and Poisson’s ratio were attained at volume fraction = 0.42. A simple method has been developed to predict the fibre transverse modulus and has allowed the characterisation of kenaf fibre’s elastic anisotropy. The performance of the Tsai–Pagano model in predicting the composites’ tensile modulus and Poisson’s ratio was compared with the Manera and Cox-Krenchel model. Results showed that the consideration of fibre’s elastic anisotropy in the Tsai–Pagano model yielded a good prediction of both composites’ modulus and Poisson’s ratio. Meanwhile, the Bowyer–Bader model produced a better tensile strength prediction owing to the inclusion of fibre length and orientation factors in the model.