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There have been many efforts using image analysis algorithms to study cardiac kinematics, or using biomechanics strategies to study myocardial material properties. In this paper, we propose a novel stochastic mechanics strategy and an extended Kalman filter (EKF) computational framework to estimate the cardiac kinematics functions and material model parameters simultaneously, given a particular a priori myocardial material model with uncertain parameters and a posteriori noisy imaging/imaging-derived data. We address the issues concerning the data-dependent uncertainty of the constraining mechanical models (and their parameters), which are needed in the ill-posed problems. Because of the periodic nature of the cardiac dynamics, we conclude experimentally that it is possible to adopt this physical-model based optimal estimation approach to achieve converged estimates. Results from canine MR phase contrast images and linear elastic model are presented.