Localized deformation and instability is the focal point of research in mechanics. The most typical problem is the plastic analysis of cylindrical bar necking and shear band under uniaxial tension. Traditional elasto-plastic mechanics of infinitesimal deformation can not solve this problem successfully. In this paper, on the basis of S(strain)-R(rotation) decomposition thorem, the authors obtain the local strain distribution and progressive state of axial symmetric finite deformation of cylindrical bar under uniaxial tension adopting nonlinear gauge approximate method and computer modeling technique.