The Cross model is a general viscous fluid model, since it is only dependent on the rate of deformation. This model is not a function of the stresses.
In principle, a viscoelastic model should be able to correctly describe the different viscoelastic effects, such as the steady state shear viscosity (left figure, green curve; right figure, open symbols), the steady state elongational viscosity (left figure, red curve), and the first normal stress difference in shear (right figure, closed symbols).