This contribution assesses the influence of stress anisotropy on stiffness using discrete element method (DEM) simulations of true-triaxial tests supplemented with analytical studies. The samples considered comprised of normally consolidated random monodisperse samples. The simulations were carried out at four different mean stress levels; at each stress level, various combinations of the three principal stresses were considered. Stiffness was measured using planar wave propagation simulations. Using regression analysis it is shown that density effects can be considered using void ratio correction factors derived for isotropically compressed samples. However, a void ratio correction factor that considers coordination number is seen to be more marginally appropriate than the conventional form used in geotechnical experimental work. Material exponents that quantify the influence of each stress component on the stiffness were then determined. Analytical expressions derived from effective medium theory are less effective than the correction functions following the form used in the current experimental practice.