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• A new unified constitutive model is proposed to describe the thermomechanical response of solder. • The model is capable of predicting the in-phase (IP) and out-phase (OP) hysteresis loop of solder under thermomechanical symmetrical loading very well. • The model can accurately simulate the thermo-mechanical ratcheting behavior under IP, OP, and isothermal loading conditions. To describe the mechanical properties of SAC305 under comprehensive loading conditions, a new model was proposed based on the internal variable theory. The tensile property of SAC305 can be normalized by dividing the stress with the saturated stress. The flow law and kinematic hardening rule can be determined by relating the property to the evolution of internal variables. Since SAC305 had no obvious yield stress, strain hardening/softening was simulated by the evolution of drag stress. The model can be used to accurately simulate the hysteresis loop and ratcheting tests at constant temperature. However, the unified model greatly overpredicted the ratcheting strain associated with thermomechanical ratcheting. Thus, a correlation term for the rate of temperature change must be introduced to adjust the back stress with changing temperature. Therefore, the modulus of back stress will be less than that of saturated stress during the entire loading process. By correlating with the kinematic hardening rule, the model could be used to simulate the thermo-mechanical ratcheting behavior, and the results were well in agreement with experimental results. Image, graphical abstract [ABSTRACT FROM AUTHOR]