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For modeling the solid-solid transformation using the phase-field method, we need to describe the phase-fields strain and stress fields in the interfacial regions which are necessary to define the mechanical driving force density of the phase-fields motion.Seeking quantitative modeling, we introduce briefly a multi-phase-field elasticity model based on the rank-one convexification of the pairwise energies which satisfies the pairwise interfacial static equilibrium and kinematic compatibility conditions. As an application, we simulate the martensitic transformation in a two-dimensional polycrystalline SMAs at small strains. The finial evaluated microstructure consists of stress-free laminates meeting the theoretical expectations.