Abstract: Two generalized variational principles on nonlinear theory of elasticity with finite displacements in which the σ_ij_i e_ij and u_i are all three kinds of independent functions are suggested in this paper. It isprovedthat these two generalized variational principles are equivalent to each other if the stress-strain relation is satisfied as constraint. Some special cases, i.e. generalized variational principles on nonlinear theory of elasticity with small deformation, on linear theory with finite deformation and on linear theory with small deformation together with the corresponding equivalent theorems are also obtained. All of them are related to the three kinds of independent variables.

Key words: finite displacement, nonlinear theory of elasticity, generalized variational principle, three kinds of independent variables