The dependence of core plasma impurity transport on the Z number has been investigated for ASDEX Upgrade H mode discharges. For the elements Ne, Ar, Kr and Xe the diffusion coefficient in the centre is D ⩽ 6 × 10-2m2/s and rises with the radial distance from the centre. With increasing Z number the transport becomes strongly convective with inward directed drift velocities that produce very peaked impurity densities for high Z. The inward drift decreases with decreasing deuterium density gradient. Neoclassical transport of the impurities has been calculated numerically. The calculated diffusion coefficient and drift velocity are close to the experimental values for the lower-Z elements Ne and Ar. However, for high Z, the calculated diffusion coefficient is smaller by a factor of up to 2.5 and the inward drift velocity is too small by a factor of 10. Toroidal rotation of the plasma that leads to an increased impurity density on the outboard side of the flux surfaces is not taken into account by the neoclassical calculations. Inboard/outboard asymmetries are not present for Ar and Ne with toroidal Mach number Mtor around 1. However, for heavier elements than Kr with Mtor ≈ 2 and an outboard/inboard ratio of ≈ 1.5, poloidal variation of the impurity density is important and might account for the discrepancy between the measured and calculated transport coefficients.