Abstract: This paper gives the contrast studies on the mechanical models of the 3 piece of analytic formulae for elastic frozen wall of shaft sinking, and illustrate the two methods to solve mechanical interaction problem between frozen wall and surrounding rock with diagraph based on superposition principles. The basic law are revealed, that the load on frozen wall varies with their own thickness and rigidity. Upon the analysis of thickness difference calculated by the three formulas, the way of “heavy liquid formula” to evaluate the load on frozen wall of Lame formula is proved unreasonable. One proposal is put forward to evaluate initial stress field based on the principle of gravity fields and Terzaghi effective stress. The relationship between the original horizontal ground load and thickness of frozen wall illustrated by three formulas are shown with a practical example. The limitation of elastic design are studied with the mathematical principles of value region and domain，which are endowed with engineering meaning. The practical usage for the application condition of elastic design are further discussed deliberately.

Key words: shaft sinking with freezing method, frozen wall, deep shaft, Lame solution