We compute the Kubo conductivity for mesoscopic quantum Hall samples taking into account the Coulomb interaction at the level of a Hartree-Fock approximation. We first explain how to compute the conductivity by rewriting the matrix elements of the position operator in terms of phase-shifted wave functions. Next, varying both magnetic field B and charge density n(e), we can show that the resulting conductivity data is very different from a non-interacting approach. Regions around the quantum Hall plateaus at integer filling factors remain quantized and the range of these quantized regions agrees with estimates based on a breakdown of screening condition. However, in the transition regions of linear screening, we find no evidence for stripes in the conductivity, contrary to recent experiments (D. H. Cobden et al., Phys. Rev. Lett. 82, 4695 (1999), T. Machida et al., Phys. Rev. 63(4), 045318 (2001) [1,2]). This, together with an argument given in , seems to suggest an effect beyond numerically tractable system sizes. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.