Despite real applications having complex triaxial loading, current physical test methods to predict component behaviour are mainly uniaxial. But previous work has indicated that there may be substantial differences between the rubber's uniaxial and biaxial behaviour and hence through incompressibility, its triaxial properties. In order to quantify these differences equipment was developed to assess the biaxial performance of selected rubber compounds using inflated circular diaphragms. Although allowing higher extensions than stretching a sheet in its own plane, such tests do not allow stress and strain to be measured directly, requiring careful marking of the sample, or calculation through simulation. On the grounds of perceived accuracy, the latter was chosen, requiring accurate, general, elastic constants to high extensions. In this thesis the development of this apparatus, along with the associated techniques is described, along with the development of a new elastic theory. The tests on this new apparatus indicated significant differences between the uniaxial and biaxial strength and fatigue of rubber. In a unimdal test natural rubber (NR) is much stronger than styrene butadiene rubber (SBR) below 35pphr of carbon black. In a biaxial test though the converse is true, although there is some evidence of crystallinity in NR during the biaxial test. Distinct differences were also found in fatigue between the two load cases. When plotted against extension ratio the biaxial life of SBR was found to increase, while the converse is true for NR. However if life is plotted against a function of strain energy, the biaxial life of both polymers increases for a given energy.