Abstract: There are two modes in the context of structure failures, material softening and geometric softening. Traditional structural theory can only analyze material-softening problems, but can not solve geometric-softening problems due to geometric displacement. In order to analyze geometric displacement possibly generated in structures, theory of geometric-displacement analysis and methods are studied. Base on virtual work principle, structural equilibrium equation and corresponding critical equation are obtained, by which equivalent unbalanced equation is deduced. Base on system deformable-consistent term introduced and three types of definite conditions summarized, the equivalent unbalanced equation can be solved and geometric displacement can be computed. The theory and methods studied can be used to analyze generalized-stability problems and has been successfully applied to the shape-forming analysis of practical cable structures.