In order to assist surgeons during minimally invasive interventions on the beating heart, it would be helpful to develop a robotic surgery system, which synchronizes the instruments with the heart surface, so that their positions do not change relative to the point of interest (POI). The synchronization of the robotic manipulators requires an estimation of the heart surface motion. In this paper, a modelbased motion estimation of the heart surface is presented. The motion of a partition of the heart surface is modelled by means of a thin or thick vibrating membrane in order to represent the epicardial surface or the connected epicard and myocard. The membrane motion is described by means of a system of coupled linear partial differential equations (PDEs), whose 3D-input function is assumed to be known. After spatial discretization of the PDE solution space by the Finite Spectral Element Method, a bank of lumped systems is obtained. A Kalman filter is used to estimate the state of the lumped systems by incorporating noisy measurements of the heart surface. Measurements can be the position or velocity of sonomicrometry-based sensors or of certain landmarks, which are tracked by optical sensors. ... mehrWith the model-based estimation it is possible to reconstruct the entire partition of the heart surface even at non-measurement points and thus at each POI.