Over the last century, several different theoretical models have been proposed for the calculation of the transverse modulus of fibres or cylinders from compression experiments. Whilst they all give similar results, the differences are significant enough to cause errors in computer simulation predictions of composite properties, and hence the issue warrants further investigation. Two independent approaches were applied to clarify this. Firstly, using an experimental approach, compression tests have been carried out on model elastic cylinders of poly(methyl methacrylate) as well as cuboids machined from the cylinders. The transverse modulus of this hard elastic material was determined directly from compression experiments on the cuboids and by analysis using different models for the cylinder compression data. Since machining was shown to change the modulus by virtue of relieving stresses in the samples, comparison was made between cuboids and machined cylinders. The transverse modulus obtained by direct compression of the cuboids was statistically equivalent to that obtained from the cylinders using the Morris model and was within 8% of the value obtained using the model derived by Jawad and Ward, as well as the mathematically equivalent models derived by Phoenix and Skelton and Lundberg. Finally, the separate and independent approach of finite element numerical modelling was also utilised. The finite element approach gave results that lie between the Jawad and Ward and Morris models. The close agreement in the outcomes of the finite element modelling and the experimental approach leads to the conclusion that the most accurate of the different analytical models are the equations by Morris as well as those due to Jawad and Ward, Phoenix and Skelton and Lundberg.