A new dynamic FEM-based subdivision surface model is proposed to reconstruct and track shapes of interest from multi-dimensional medical images. The model is based on the butterfly subdivision scheme, a popular subdivision technique for generating smooth C¹ (first derivative continuous) surfaces of arbitrary topology, and is embedded in a physics-based modeling paradigm. This hierarchical model needs very few degrees of freedom (control vertices) to accurately recover and track complex smooth shapes of arbitrary topology. A novel technique for locally parameterizing the smooth surface of arbitrary topology generated by the butterfly scheme is described; physical quantities required to develop the dynamic model are introduced, and the governing dynamic differential equation is derived using Lagrangian mechanics and the finite element method. Our experiments demonstrate the efficacy of the modeling technique for efficient shape recovery and tracking in multi-dimensional medical images.