The physical concept of structural stability sets up the foundation for anti-buckling concept design and stability check of structures. The correlations between disturbed configurations of the initial straight column and a rigid ball initially settled in the origin of a given support surface have been established by developing an equivalent rigid ball model for the stability analysis of an idealized column. Such a model is designed to facilitate students and structural engineers to intuitively understand stability of elastic systems. Furthermore, an incremental generalized force criterion has been proposed to identify the static stability of axial compression member with arbitrary end constraints, which provides physical explanation to disturbance generalized resistance and equilibrium stability of a multiple degree of freedom system. It can be used to determine the stability of an intermediate state of a nonlinear equilibrium path of structures and to indicate the post-buckling equilibrium configurations of structures.