Abstract: Generalized reciprocal theorems of non-coupled and coupled systems, which are valid for two deformed bodies with different constitutive relations are established by generalizing the idea of Betti’s reciprocal theorem. When the constitutive relations of the two deformed bodies are all alike and linear elastic, the generalized reciprocal theorem of non-coupled systems just becomes Betti’s. Meanwhile, the generalized reciprocal theorems are applied to simulate calculations in elasticity.