The age hardening and age softening of nine solution-treated and subsequently cold-rolled Al–(1–3)Mg–(0–0.4)Cu–0.15Si–0.25Mn (in wt%) alloys with potential applications in both packaging and automotive industries have been investigated. Cold work levels were 10%, 40% and 90% reduction. The proof strengths of the aged alloys range from 130MPa to 370MPa. A physically based model for yield strength has been developed which includes a one-parameter dislocation evolution model to describe work hardening and recovery and a two-precipitate precipitation-hardening model. The model is based on analytical equations, avoiding computing time-intensive iterative schemes. An exceptionally high model accuracy has been demonstrated. The model parameters are verified by transmission electron microscopy and calorimetry analysis of the materials.