M.Ing. (Mechanical Engineering) / This dissertation evaluates the suitability of the finite element method as a tool for the design and analysis of elastomeric materials in general and flexible shaft couplings in particular. The theoretical background covers numerous aspects that are essential to the comprehension of the functioning of elastomeric materials and the difficulties inherent to the numerical modelling of such materials. These aspects include the properties of rubber, the functioning and selection of flexible couplings and some details regarding linear -, non-linear - 'and dynamic finite element analysis. The problems investigated for the purposes of this study may be divided into three categories: • The capabilities of the finite element method to compare different variations of a flexible coupling design parametrically is investigated. • Uni-axial tensile - and compressive material tests are numerically simulated to assess the ability of the finite element method to predict the response of materials subjected to large-scale nonlinear deformation. The numerical results are also verified by means of physical material tests. • Based on the modelling methods that were optimized in the first two categories, a numerical model of a flexible coupling in start up mode is developed. The accuracy of predictions is evaluated by comparison with physically measured results.