A cross-anisotropic formulation for elasto-plastic constitutive models based on a non-uniform scaling of the stress tensor is described. Taking advantage of the material symmetries characterising cross-anisotropy, only two scaling factors, one for the normal stress components and one for the shear stress components, are required. It is shown that the formulation can be easily introduced in already implemented models with minor modifications. The performance of this formulation is investigated by reproducing the strength variation of anisotropic rocks in triaxial tests. The numerical simulation of an unsupported excavation is also presented to show the effect of different scaling factors and bedding plane orientations.