In this study, the constitutive behaviour for creep performance of 95.8Sn–3.5Ag–0.7Cu lead-free solder joints was investigated. It was observed that the stress exponent (n) can be well defined into two stress regimes: low stress and high stress. A new, improved constitutive model, which considered back stress, was proposed to describe the creep behaviour of SnAgCu solder joints. In this model, the back stress, which is a function of the applied shear stress in the low stress regime (LSR) and a function of the particle size, volume fraction and coarsening of IMC particles in the high stress regime (HSR), was introduced to construct the relationship between the creep strain rate and the shear stress. The creep mechanism in these two stress regimes was studied in detail. In the LSR, dislocations passed through the matrix by climbing over the intermetallic particles, while in the HSR, the dislocations were glide-controlled. According to the different creep mechanisms in both the stress regimes, the back stress was calculated, respectively, and then incorporated into the Arrhenius power-law creep model. It was demonstrated that the predicted strain rate–shear stress behaviour employing the modified creep constitutive model which considered back stress, was in good agreement with the experimental results.