In the case of plastic buckling of a structure, the critical state largely depends upon the initial deflection; this makes the load in the critical state decrease. In the present paper, as regards column and plate with initial deflections, their behavior under compressive load is theoretically investigated, by using the so-called Shanley model and the extended Shanley model for plate. Even if the critical stress for column or plate without any initial deflection is within the elastic range, the existence of the initial deflection makes the critical stress decrease. In the case of the plate with small initial deflection, it is confirmed that“the greatest lower bound of the Kármán state” proposed by the present author in his previous paper [5] is regarded as the critical state for practical purpose ; when it is compressed one-directionally, the stress in this state is almost equal to the so-called reduced modulus stress in classical sense. Whatever the initial deflection may be, the critical stress of compressed column or plate compressed one-directionally is not less than the stress, p_eE_t∞E , where p_e is the elastic critical stress, E_t∞ is the tangent modulus corresponding to large tensile strain and E is Young's modulus.