||Cardiac motion estimation has been an important focus in medical image analysis for decades, where the goal is to recover the kinematic properties of the in vivo hearts from noninvasive image sequences. Clinically relevant information, including the possible locations and extents of tissue infarctions caused by heart diseases, can then be extracted by identifying the kinematics abnormalities of the myocardium. In order to obtain sensible estimates of the myocardial kinematics based on biomechanical constraints, proper spatial and temporal models should be adopted according to the realistic physical properties of the cardiac tissues. Spatially, the large deformation of the heart wall as well as the fibrous structure of the myocardium should be carefully considered for proper deformation and material modeling. Temporally, uncertainties in the system modeling and the data measurements should be handled by using the multiframe observations of the cardiac image sequences. In this thesis, we present two cardiac motion estimation algorithms under the meshfree representation and computation framework, one fur frame-to-frame estimation using finite deformation and composite material models, and the other for multi-frame estimation using infinitesimal deformation and anisotropic material models. In the first algorithm, the total Lagrangian formulation has been utilized as the deformation model, instead of the simple but unrealistic linearized deformation model which has been widely used for cardiac motion analysis. In addition, composite anisotropic material properties of the fibrous myocardium have been conveniently enforced within the meshfree particle platform. In the second algorithm, the same composite material model is incorporated with multiframe Kalman filtering, using the infinitesimal deformation model. Experiments based on synthetic data with ground truth and a canine phase contrast velocity MR image sequence have been performed, and both show very promising results.