A framework of physically based shape morphing with the multiscale wavelet descriptor is proposed. We formulate the problem of shape metamorphosis with the Lagrangian dynamic equation which simulates the deformation as a process driven by a certain force as the result of being released from strain energy. Then we show the discretization of Lagrange's equation with respect to the wavelet representation and derive the corresponding mass and stiffness matrices. We show the computation of entries of the stiffness matrix by solving a system of linear algebraic equations. Due to the multiscale representation capability of the wavelet descriptor, the graph in intermediate frames can be generated via multiresolution rendering. Experiments are conducted to demonstrate the performance of the proposed physically based morphing algorithm.