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Morphological evolutions and kinetics process controlled by transformation-induced elastic strain (include external strain field) during isostructure phase separation are systematically investigated using prototype binary alloy by diffuse-interface field model. The results show that various types of morphologies, such as basket-weave structures, sandwich-like multi-domain structures, precipitate macro lattices and plate-like structures, are predicted in different stages of phase separation. It is demonstrated that the precipitates are preferentially oriented with an external stress for an inhomogeneous elastic modulus system. Moreover, the simulation results also indicate that the small particles will be connected along elastic soft directions to formation bigger particles in the stage of growth and those small isolated particles will be consumed by bigger particles in the stage of ripening.