Elastically deformable models have found applications in various areas ranging from mechanical sciences and engineering to computer graphics. The method of Finite Elements has been the tool of choice for solving the underlying PDE, when accuracy and stability of the computations are more important than, e.g., computation time. In this paper we show that the computations involved can be performed very efficiently on modern programmable GPUs, regarded as massively parallel co-processors through Nvidia’s CUDA compute paradigm. The resulting global linear system is solved using a highly optimized Conjugate Gradient method. Since the structure of the global sparse matrix does not change during the simulation, its values are updated at each step using the efficient update method proposed in this paper. This allows our fully-fledged FEM-based simulator for elastically deformable models to run at interactive rates. Due to the efficient sparse-matrix update and Conjugate Gradient method, we show that its performance is on par with other state-of-the-art methods, based on e.g. multigrid methods.