Abstract: We present a computational efficient method for isotropic hyper elasticity based on functional analysis. By selecting a class of shape functions, we arrive at a computational scheme which yields very sparse tensors. This enables fast computations of the hyper elastic energy potential and its derivatives. We achieve efficiency and performance through the use of shape functions that are linear in their parameters and through rotation into the eigenspace of the right Cauchy-Green strain tensor. This makes near real time evaluation of hyper elasticity of complex meshes on CPU relatively easy to implement. The approach does not rely on a specific shape function or material model but offers a general framework for isotropic hyper elasticity. The method is aimed at interactive and accurate non-linear hyper elastic modeling for a wide range of industrial virtual design applications, which we exemplify by insertion of hearing aid domes into the ear canal. We validate the method for tetrahedral meshes with linear shape functions with an Ogden material model by comparing simulations to deformations of real material. We illustrate the use of other shape functions and models using uniform cubic B-splines in combination with Riemannian elasticity.