Abstract: Frozen-wall design is a success prerequisite for the freezing method, few literatures have reported, however, that side-wall displacement convergence affects frozen-wall thickness design. To consider the influence of side-wall displacement convergence, the Column-hole expansion theory was used to derive the complete formal solutions on stress and displacement for plastic frozen wall and elastoplastic unfrozen formations, and a calculation formula of frozen-wall thickness was established. An engineering case was studied by three methods, to verify the correctness of the established formulas. The effects of horizontal ground pressure, cohesion and internal friction angle of frozen soil, elastic modulus and Poisson's ratio, cohesion and internal friction angle of unfrozen soil on side-wall deformation and frozen-wall thickness were analyzed. The results show that the frozen-wall thickness difference is about 8.6% and side-wall deformation is about 0.17 at 800 m depth, considering the influence of well side displacement convergence or not, for the fully plastic frozen wall and elastic formation mechanical model. The new formula has high theoretical significance and practical value in predicting the side-wall deformation for a kilometer topsoil shaft.