Simulation techniques for deformable bodies are of major relevance for a broad range of medical applications. In recent decades, a lot of work has been performed to improve simulation methods, allowing interactivity or even real time. However, this work often focused on applications such as computer games or virtual environments, where physical accuracy is not a primary goal. The goal of this report is to give an overview of efficient physics-based techniques for deformable objects, focusing on finite element methods, and to discuss the applicability of these techniques in medical scenarios. As a result, we focus on techniques that are amenable to simulating highly resolved meshes, which for instance can be generated from computed tomography (CT) or magnetic resonance (MR) images, and we review the so-called corotated finite element method that has shown a high potential in recent years. Specifically, we will capture in detail the related work in this field and demonstrate the current state of the art in efficient deformable bodies simulations.