This paper presents a study of the strain hardening of a 7000 series aluminium alloy. A wide variety of microstructural states are tested both in uniaxial tension and by performing Bauschinger tests. Their microstructural features are evaluated quantitatively in terms of precipitate size and volume fraction using small-angle X-ray scattering. A physically-based model for strain hardening, using a modified version of the Kocks-Mecking-Estrin formalism, is presented for the precipitation states that exhibit precipitate bypassing. The model takes explicitly into account the microstructural information and describes in detail the mechanisms governing the storage, stability and annihilation of Orowan loops around the precipitates. It describes both the uniaxial and the strain-reversal tests, by evaluating separately the kinematic and isotropic contributions to strain hardening and using an appropriate mixing law. In addition, the transient of strain-reversal Bauschinger tests is discussed with respect to the effect of precipitates on strain reversibility. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.