The stability of Reut and Beck columns subjected to any combination of gravity and non-conservative (fixed-line of follower) comprenssive axial forces is presented using the dynamic formulation. The proposed method is effects of the end gravity force, translational and rotational inertias along the member. Analytical results are intended to capture the limit on the range of applicability of the static or Euler’s method in the stability analysis of slender columns, and to define the transition from static instability (with zero frequency) to dynamic instability (“flutter”). Finally, the comparison between the characteristic stability equations of slender Reut and Beck columns is presented.