Deformable object matching, which is also called elastic matching or deformation matching, is an important and challenging problem in computer vision. Although numerous deformation models have been proposed in different matching tasks, not many of them investigate the intrinsic physics underlying deformation. Due to the lack of physical analysis, these models cannot describe the structure changes of deformable objects very well. Motivated by this, we analyze the deformation physically and propose a novel deformation decomposition model to represent various deformations. Based on the physical model, we formulate the matching problem as a two-dimensional label Markov Random Field. The MRF energy function is derived from the deformation decomposition model. Furthermore, we propose a two-stage method to optimize the MRF energy function. To provide a quantitative benchmark, we build a deformation matching database with an evaluation criterion. Experimental results show that our method outperforms previous approaches especially on complex deformations.