Saint-Venant’s Principle in elasticity  has its over 100 year’s history. Boussinesq  and Love  announced general statements of Saint-Venant’s Principe. The early authors made  important contribution to the principle. Zanaboni “proved” a theorem ，trying to concern Saint-Venant’s Principle, but in the present paper we will prove that Zanaboni’s theorem is false.

Variational theory of elasticity is surveyed in the context of mathematical logic in the present paper. The problem of variable-independence of variational principles raised by Professor Chien Wei-zang is discussed. We find that Chien’s “High-order Lagrange Multiplier Theory”, which deals with the problem of variable-independence and constraint of variational principles, is inconsistent; Luo En’s system, which is involved in the problem of variable-independence, is involved in contradictions; the conventional understanding of independence of variables of variational principles connotes contradiction.

In this article the history of development of Saint-Venant’s Principle is reviewed, referring to the most important events concerning the principle as the historical clue, and the important works and results are evaluated; the view-points that Toupin Theorem can not be considered as a mathematical expression of Saint-Venant’s Principle and that the general Saint-Venant’s Principle does not stand, but modified Saint-Venant’s principles can be proved true are published and explained; the mathematical approaches for eslablishing modified Saint-Venant’s principles are summarized; the significance of proving  the principle is expounded; in order to bring  those essential issues and discussions concerning the principle to attentio

Zanaboni  Theorem  Is  Not  True

Saint-Venant's Principle is important in the theory and application of elasticity and its proof or formulation is a major attraction  for authors. Among others，Toupin's Theorem plays  the most influential  role in the history of  development  concerning Saint-Venant's Principle.

The paper titled "The Study by Mr.