This paper is inspired by two articles on the title subject, namely by Koiter and by Sugiyama, Langthjem and Ryu. The former warned the engineering community to beware of the above forces. The latter maintained that these forces are realistic. It is hoped that this review sheds some additional light on an issue that seems to perplex many students of dynamic stability. The paper does not contain any new information unknown to researchers; it represents a critical review of pertinent papers dedicated to the topic of dynamic stability of structures under so called “follower” forces. The attempt here is to present an account of the literature in a manner that is both objective and humble. This paper reviews both the theoretical and experimental contributions to the theory of nonconservative problems with a single objective in mind, to attempt to answer a nagging question “Is the model of the statically applied follower forces useful?,” that arose due to the papers by Koiter and Sugiyama, Langthjem and Ryu. This article explores the static and dynamic stability criteria as pertaining to the nonconservative problems; the experimental side of the problem; the results pertaining to Beck’s column placed on homogenous or inhomogeneous elastic foundations; and criticisms expressed in the literature about the result on the immunity of the instability load to the Winkler foundation modulus: The paper then discusses Koiter’s ideas on nonconservative instability problems, and attempts to provide insights on the abovementioned question. Special emphasis is placed on pipes conveying fluid with or without an elastic foundation. It then summarizes the literature on the “follower forces.” Such a summary is inevitably incomplete because of the huge literature accumulated so far on the nonconservative problems in the theory of elastic stability. There are 202 references cited in this review article, and a supplementary bibliography is provided.

*Nonconservative Problems in the Theory of Elastic Stability*, Fizmatgiz Publishers, Moscow (in Russian) (English translation, Pergamon, New York, 1964).

*Theory of Elastic Stability*, McGraw–Hill, Auckland, p. 156.

*Principles of Structural Stability*, Waltham, MA.

*Stability of Elastic Systems*, Sijthoff and Noordhoff.

*Proceedings of the Leningrad Polytechnic Institute*, No. 192, pp. 21–27 (in Russian).

*Proceedings of the Odessa Institute of Civil and Communal Engineering*, No. 1.

*Proceedings of the Odessa Institute of Civil and Communal Engineering*, No. 1 (in Russian).

*Stabilita¨tsprobleme der Elastostatik*, Springer-Verlag, Berlin, p. 217 (in German).

*Stability and Vibrations of Elastic Systems*, Nauka, Moscow, p. 131 (in Russian, 4th ed.).

*Works in Mechanics*, Gostekhizdat, Moscow, pp. 436–454 (in Russian).

*History of the Theory of Elasticity*, Cambridge University Press, Vol. 1, pp. 39–50.

*Selected Problems and Questions in Strength of Materials*, Gostekhizdat, Moscow, pp. 44, 183, and 184 (1st ed., in Russian).

*On Elastic Stability Under Nonconservative Forces*, University of Waterloo Press, Waterloo, Ontario, Canada.

*Problems of Stability in Structural Mechanics*, edited by V. V. Bolotin, I. M. Rabinovich, and A. F. Smirnov, Izdatelstvo Literatury po Stroitelstvu, Moscow, pp. 68–84 (in Russian).

*Nonlinear Stability of Structures*, A. N. Kounadis and W. B. Kra¨tzig, eds., Springer-Verlag, Vienna, pp. 3–72.

*Ten Lectures-Conversations on Strength of Materials*, Nauka, Moscow (in Russian).

*Can Theories Be Refuted*?, Kluwer, Dordrecht.

*Can Theories Be Refuted*?, S. Harding, ed., Kluwer, Dordrecht, pp. 205–247.

*Stability of Equilibrium of Elastic Systems*, GITTL, Moscow (in Russian), pp. 161–162.

*31st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference*, Paper AIAA-90-0948, Long Beach, pp. 1893–1898.

*Buckling Experiments*,

**1**, pp. 1–3, Wiley, London (Vol. 2, 2002).

*Proceedings of the Sixth National Science Congress*, The Scientific and Technical Research Council of Turkey, pp. 301–311.

*Thoughts About Science and About Scientists*, Nauka, Moscow (in Russian), p. 50.

*Proceedings of Second All-Union Congress on Theoretical and Applied Mechanics*, Jan. 30–Feb. 5, 1964, Nauka, Moscow (in Russian), Vol. 3, pp. 276–294.

*Flow-Induced Vibration of Circular Structures*, Hemisphere, Washington, DC.

*Flow-Induced Vibrations*, Van Nostrand-Reinhold, New York.

*Fluid-Structure Interaction, Slender Structures and Axial Flow*, Academic, London.

*Proceedings of the 10th U.S. National Congress of Applied Mechanics*, J. P. Lamb, ed., pp. 155–170.

*Stability Theory*, Academic, New York.

*Proceedings of the 2nd International Congress in the Aerospace Sciences*, Zuerich, Sept. 12–16, pp. 911–925.

**No. 4**(in Russian).

*Proceedings of the 8th Southeastern Conference on Theoretical and Applied Mechanics*, Virginia Polytechnic Institute, pp. 379–389.

*Proceedings, of the 3rd World Congress of Structural and Multidisciplinary Optimization*, May 17–21, Buffalo, New York.

*Proceedings of the Third World Congress of Structural and Multidisciplinary Optimization*, May 17–21, Buffalo, New York.

*Handbook of Experimental Stress Analysis*, 1st ed., Wiley, New York.

*Experimental Mechanics, William M. Murray Lecture 1967*,

**8**(3), pp. 97–106.

*Proceedings of the 4th U.S. National Congress of Applied Mechanics*, ASME, New York, pp. 15–33.

*Instability of Continuous Systems*, edited by H. Leipholz, Springer, Berlin, pp. 349–360.

*The Neglect of Experiment*, Cambridge University Press, London.

*Stability of Structures*, Oxford University Press, New York.

*Instability of Continuous Systems*, H. Leipholz, ed., Springer, Berlin, pp. 240–247.

*An Introduction to Chaotic Dynamical Systems*, Addison-Wesley, Reading.

*Instability of Continuous Systems*, H. Leipholz, ed., Springer, Berlin, pp. 96–111.

*Nonlinear Stability of Structures*, edited by A. N. Kounadis and W. B. Kra¨tzig, eds., Springer Verlag, Wien, pp. 143–168.

*Mechanics in the SSSR in 50 Years*, Nauka, Moscow (in Russian).

*Proceedings of the 26th Israel’s Mechanical Engineering Conference*, May 21–22, pp. 495–497.

*Proceedings of the 26th Israel’s Mechanical Engineering Conference*, May 21–22, pp. 209–211.

*Stability of Elastic Rods*, World Scientific, Singapore, p. 380.

*Stability of Elastic Structures*, Springer, Berlin, p. 120.

*Thought Experiments*, Oxford University Press, New York, p. 27.

*Aspects of Scientific Explanation*, Free Press, New York, p. 165.

*Popular Scientific Lectures*, 5th ed., Open Court Publishers, La Salle, IL, p. 220.

*The Intersection Between Science and Philosophy*, Y. Elkana, ed., Humanities, Atlantic Highlands, NJ.

*Proceedings of the Leningrad Polytechnic Institute*,

**278**, pp. 52–54 (in Russian).

*Fluid Mechanics for Physicists*, Cambridge University Press, p. 161.

*Hydrodynamics*, 6th ed., Cambridge University Press (reprinted in 1993).

*Model-Aided Diagnosis of Mechanical Systems*, Springer, Berlin, p. 8.

*Proceedings, IUTAM Symposium on Unilateral Multibody Contacts*, F. Pfeiffer and Ch. Glockner, eds., Kluwer, Dordrecht, pp. 233–242.

*Instability of Continuous Systems*, H. Leipholz, ed., Springer, Berlin, pp. 263–265.

**21**(

**4**), pp. 43–50 (in Bulgarian).

*Proceedings of the 41st Israel’s Annual Conference of Aerospace Sciences*, February 21–22.

*Proceedings of FSI, AE &*FIV+N, November 17–22, Paper IMACE 2002-34018, New Orleans, Louisiana.

*Can Theories Be Refuted?*, S. G. Hardling, ed., Reidel, Dordrecht, p. 1.

*Flow-Induced Vibration*, S. Ziada and Th. Staubli, eds., Balkema, Rotterdam, pp. 355–362.

*Theory of Probability: A Critical Introductory Treatment*, Wiley, New York.

*Structural Mechanics*, J. N. Goodier and N. J. Hoff, eds., Pergamon, New York, pp. 115–168.

*A Dictionary of Mathematics*, Harper and Row, London, p. 130.

*Dynamics of Elastics Structure in Conditions of a Free Flight*, Naukova Dumka, Kiev (in Russian).

*Representing and Intervening*, Cambridge University Press.

*Vibrations and Stability of Multiple Parameter Systems*, International Publishing, Alphen aan den Rijin, p. 58.

*Stroitelnaya Mekhanika i Raschet Sooruzhenii*, No. 2, pp. 76–77 (in Russian).

*The Oxford Dictionary of Literary Quotations*, p. 114, Oxford University Press, Oxford.

*Criticism of Growth of Knowledge*, I. Lakatos and D. Musgrave, eds., Cambridge University Press, Cambridge, pp. 91–196.

*Die Direkte Methode der Variationsrechnung und Eigenwertprobleme der Technik*, edited by G. Braun, Karlsruhe, p. 175 (in German).

*Stability Theory*, Teubner, Stuttgart.

*Mechanics of Deformable Solid Body*, Nauka, Moscow, pp. 43–51 (in Russian).

*McGraw-Hill Dictionary of Scientific and Technical Terms*, 3rd ed., McGraw–Hill, New York, p. 1032.

*Verification and Validation in Computational Science and Engineering*, Hermosa Publishers, Albuquerque.

**8**, 337–362.

*Proceedings of the Second World Congress of Structural and Multidisciplinary Optimization*, W. Gutkovski and Z. Mroz, eds., Vol.

**1**, pp. 399–404.

*Instabilities and Catastrophes in Science and Engineering*, Wiley, New York.

*Vibrations and Stability*, McGraw–Hill, London.

*New Concise Webster’s Dictionary*, Modern Publishing, p. 210.

*The Jerusalem Post International Edition*, November 30.

*Proceedings of the Sixth International Conference of Composite Materials*, ICCM VI, England,

**5**, 38–5.46.

*Advances in Applied Mechanics*, Academic, New York, Vol.

**4**, pp. 351–403.