Uniaxial unconstrained compression experiments have been conducted on porcine, bovine and ovine muscle samples oriented in the fibre, non-fibre and 45° from the fibre direction. The porcine and bovine samples were aged tissues. The ovine samples were fresh tissues. A transversely isotropic hyperelastic model and a model which uses the theory of transverse isotropy and strain dependent Young’s moduli have been fitted to the experimental data. The results show that the hyperelastic model does not adequately fit the data in all three directions of testing. In contrast, the strain dependent Young’s moduli model (SYM) gives a good fit to the experimental data in both the fibre and non-fibre direction up to 30% strain for porcine and bovine samples. The model also yields a very good prediction of the behaviour of the muscle at 45° from the fibre direction. However, preliminary data from the fresh ovine samples indicates that the SYM may not be a suitable model for description of the material properties of very fresh tissue.