Five methods are used to measure values of circumferential Young’s modulus and three methods are used to obtain shear modulus using the closed and open ring specimens. Based on the assumption that the technique using a strain gage must yield the correct value of Young’s modulus, the technique using a closed ring specimen gives more consistent results than the technique using an open ring specimen. For the simplicity of measurement, the technique using a closed ring specimen under compression can be used as long as the thickness of the used specimen remains thin enough to neglect the effects of shear deformation. To measure the shear modulus, G12, both techniques using the open and closed ring seems to have the same trend as a function of thickness. As expected from the loading scheme, the technique using an open ring gives more consistent results for the shear modulus.