A rigorous identification of low-dimensional models for thin structures is considered. The author starts from a rigorous approach to a dimension reduction problem in the framework of nonlinear elasticity. The purpose is to deduce some linearized reduced models for thin plates in the framework of finite plasticity. First, the author examines the asymptotic behavior of almost minimizers of three-dimensional energies as a small parameter tends to zero. It is a quite subtle issue which requires some compactness results and limit inequalities. Further, the author shows that the lower bounds obtained are optimal. Finally, the convergence of almost minimizers of three-dimensional energies is discussed, and some examples are given.