Organ motion due to respiration and contact with surgical instruments can significantly degrade the accuracy of image-guided surgery. In most applications, the ensuing soft tissue deformations have to be compensated in order to register preoperative planning data to the patient. Biomechanical models can be used to perform registration based on sparse intraoperative sensor data. Using elasticity theory, the approach can be formulated as a boundary value problem with displacement boundary conditions. In this paper, we propose to use corotated finite elements (FE) with quadratic shape functions as a robust and accurate model for real-time soft-tissue registration. A detailed numerical analysis reveals that quadratic FE perform significantly better than linear corotated FE for high resolution meshes. We also show that the method achieves nearly the same registration accuracy as a complex nonlinear viscoelastic material model. Furthermore, a phantom experiment demonstrates how the model can be used for intraoperative liver registration.