Simulation of thin elastic surfaces is an essential component of applications ranging from cardiovascular medicine to flapping wing aerospace engineering. Consequentially a vast array of approaches exist for such problems. Despite this, few approaches exist to model elastic surfaces in an Eulerian context - a significant hindrance to Eulerian fluid structure interaction techniques. We introduce a fully Eulerian method for accurately simulating elastic surfaces. Our approach can be applied to membranes and shells with nonlinear elastic properties, moving under their own dynamics or immersed in a fluid. The new approach is also compatible with state of the art level set techniques, and can make use of high-order finite difference stencils or more sophisticated techniques. We present the method including implicit imposition of internal boundary conditions and results for a range of model problems.