An analytical method of dynamic instability of three-dimensional framed structures to which it is difficult to apply the theory of continuum mechanics is proposed in the two cases of regarding and disregarding the effect of damping, in the cases where the effect of forced vibration is neglected. The equations of motion of Mathieu-Hill type are set up using the linearized finite displacement method, and the equations of boundary frequency in the regions of dynamic instability of columns and arches are derived applying the proposed method. The results show good agreement with the boundary values of a column simply supported at the both ends.