Abstract: The purpose of this paper is to give a systematic way of deriving various generalized variational principles in elasticity, and also to give some applications of these principles for improving the finite element techniques. It is, however, easy to apply these methods for solving problems in other fields. In the first, it is indicated that the functionals of these generalized variational principles can be obtained systematically by means of Lagrange multiplier method. The physical meaning of these multipliers can be determined uniquely through the variation processes. In this way, it is possible to eliminate the difficulty of finding the functionals in generalized principles. In the second place, through Lagrange multiplier method, it is possible to establish various derived variational principles with fewer conditions of variation than those of the original variational principle. These derived variational principles with fewer conditions of variation may be called the incomplete generalized variational principles, on the other hand, we may call the derived variational principles without any conditions of variation the complete generalized variational principles, or briefly the generalized variational principles. It is possible to establish various generalized variational principles, either completely or incompletely, for small displacement theory of elasticity, including two well-known generalized variarional principles derived from the principle of minimum potential energy, and from the principle of minimum complementary energy. The equivalence of these two generalized variational principles is proved. These generalized principles include also Hellinger (1914) [1]-Reissne (1950)[2] principle and H. C. Hu-Wushizu (1955) [3][4] principle. In is also possible to establish principles of potential energy and complementary energy in finite displacement theory of elasticity, and various related incomplete generalized variational principles. The equivalence of these generalized variational principles derived from minimum potential energy and from minimum complementary energy has also been proved in the finite displacement theory. In this paper, the well-known applications of generalized variational principles to finite element method are discussed. Three more ways of applications are also given.