Abstract: Acquiring the characteristics of the Earth's deformation induced by the internal and external forces is the key to recognizing the Earth's internal structure and dynamic processes. Observing and investigating the global and regional deformation is one of the important tasks for constructing and maintaining a high precision space-time reference. This paper introduces in details the main progress in the theoretical modeling of the Earth's deformation. The emphases are on the loading effects of the atmosphere, oceans, land water and heat, as well as the deformation caused by seismic dislocation. The main points involve the fundamental theory of (heat) elastic deformation, the efficient methods to the solution and the difficulties in the computation, as well as the solving strategies to these difficulties. Finally, on the basis of the elastic deformation, we prospect the requirements and potential applications of the Earth's deformation theories under the background that the accuracies of the instruments are more and more improved and human's activities intensively affect the global environment.

Key words: SNREI Earth, elastic deformation of the Earth, surface loading of the Earth, seismic dislocation