Real-time simulation of surgery requires fast and realistic modeling of deformable objects. However today, few models are available, they are still time costly and limited in number of tetrahedra by algorithm complexity. We present here a framework to design algorithms adapted to any kind of hypere-lastic models, which include Saint Venant-Kirchhoff, Neo-Hookean and Mooney-Rivlin, handling large deformations and large displacements. Moreover , the algorithm complexity is linear in the number of tetrahedra; a comparison in number of operations performed with an existing algorithm on a similar case shows a gain of more than 40 times faster.