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This paper presents a deformable object tracking algorithm based on the boundary element method (BEM). BEM differs from the finite element method (FEM) in that only the boundary of the object needs to be meshed for BEM. FEM requires that the interior of the object is meshed in addition to its boundary. This feature of BEM makes it attractive for computer vision problems. We present a deformable template that uses BEM to model deformations. This deformable template is registered to an image using an energy minimization approach. The BEM tracking algorithm presented in this paper constraints the tracking results to satisfy the condition of static equilibrium. This increases the robustness of the tracking results and enhances the usefulness of the forces obtained from the tracking procedure. We demonstrate the tracking performance of this algorithm for objects with linear and non-linear elastic properties. In addition, the results of tracking the deformations of a cell are presented.