In the current work we present the results of 3D micromagnetic modelling of magnetostrictive strain and magnetic hysteresis under uniaxial stress in ferrite. The simulations are performed on artificial microstructures with different grain orientations that allow to take into account the anisotropy of magnetic and mechanical properties of iron-based alloys. The obtained results are in reasonable agreement with experimental observations. The proposed method opens a path to predictive modelling of the magnetic properties of different textured steels in the context of in-line non-destructive testing.