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Sn-Ag-Cu based solder alloys are replacing Sn-Pb solders in electronic packaging structures of commercial electric devices. In order to evaluate the structural reliability, the mechanical property of solder material is critical to the numerical simulations. Annealing process has been found to stabilize material properties of Sn-37Pb solder material. In the current study, the annealing effect on tensile behaviour of Sn-3.0Ag-0.5Cu (SAC305) solder material is investigated and compared with Sn-37Pb solder. It is found that the tensile strength for both materials are more stabilized and consistent after the annealing process, nevertheless, the annealing process will improve the plasticity of SAC305 solder dominated by dislocation motion, and impede the occurrence of hardening deformation in Sn-37Pb solder dominated by grain-boundary sliding mechanism. Furthermore, the annealing effect is quantified in the proposed constitutive model based on unified creep-plasticity theory. The parameters are calibrated against the measured stress-strain relationships at the tensile strain rates ranging from 1 × 10−4 to 1 × 10−3 s−1. The numerical regressions for dominant parameters in the proposed model reveal the intrinsic differences between SAC305 and Sn-37Pb solders under annealing treatment. [ABSTRACT FROM AUTHOR]