In this chapter the fundamental differences between two principal approaches of structural mechanics, namely Galileo (limiting state) and Navier (working state) approaches, are considered. The concept of the limiting state from our modern point of view is discussed. The contribution to the development of structural mechanics by outstanding scientists is emphasized like J.L. Lagrange, S.D. Poisson, L. Euler, B.P. Clapeyron, G. Lame, J.W. Rayleigh, J. C. Maxwell, and H. Helmholtz, to name but a few.
