Abstract: The main objective of this paper is to study minimization methods for coupled problems in the following two directions:(1)to establish two minimum principles for the coupled thermo-elastodynamics:(2)to provide, for a wide class of coupled physical systems,an algorithm to construct the appropriate minimization functions.The main idea of the paper consists in the following steps:(1) to reduce the number of governing equations by elimination and the convolution theory;(2) to separate coupled variables using potential operator defined in a real Banach space ;(3) to derive a transformed minimum principle for Laplace transformation;(4) to establish the minimizing functional by the introduction of the set of admissible weight functions to the original space-time domain . The results of this paper are of great significance on constructing minimizing functionals for a wide class of coupled systems.