•The paper provides the first documented simulation of extruded Mg plate during the cyclic loading.•Correlations among the strain hardening plateau, subsequent rapid strain hardening, and twin reorientation are clarified.•Different CRSS values for twin nucleation and twin growth/detwinning are used in the EVPSC model.•The monotonic strength and strain hardening anisotropy are well-predicted along multiple directions.•Diffraction peak intensity evolutions and lattice strain evolutions are predicted during the cyclic loading. A recently developed crystal plasticity model for describing twinning and detwinning behavior is employed to simulate the behavior of extruded Mg alloy, ZK60A. Notably, accounting for the initial texture and calibrating the model using tension and compression along one direction permits prediction of the strength anisotropy, strength asymmetry, and strain hardening behavior along other directions, for cases for which the contribution of twinning is large, small and intermediate. The model discriminates between the stress required to initiate twinning and that required to grow (thicken) previously existing twins. This enables the model to simulate the unusual stress–strain hysteresis behavior during twinning (e.g., sharp yielding behavior) as well as that of detwinning (characterized by quite gradual yielding). The strain hardening plateau which occurs during both twinning and detwinning are captured, as are the rapid hardening induced by the exhaustion of these mechanisms. Finally, the modeling is validated using previously published in-situ neutron diffraction data. The predicted diffracted intensity evolution, which is indicative of the volume fraction of twinning compares well with the experimental data. For the first time, the lattice strain evolutions during cyclic loading (involving twinning and detwinning) of an extruded magnesium alloy are predicted. Most features of the experimentally observed internal strain evolution are well-described. In particular, the inflections which may be associated with the initiation of particular deformation mechanisms: basal and non-basal slips, as well as deformation twinning are predicted. Careful analysis of the lattice strains reveals greater than expected load sharing by the precipitate phase.