We examine a numerical technique developed to simulate unsteady dispersion and diffusion in coated tubes of arbitrary but axially-constant cross-section. The method is validated against analytical asymptotic solutions produced for tubes of circular section, then applied to the study of dispersion in equivalent tubes of square section, coated on one, two, three or four walls, and in a family of tubes of rectangular section, again with stationary phase coating on one wall. The results show that both the sectional geometry and coating regime have a profound influence on the axial dispersion, and hence on the efficiency of associated chromatography. For rectangular-sectioned columns with single-wall coating, the greatest separation efficiency results when the coating is applied to one of the longer segments of the cross-sectional perimeter. Published by Elsevier Science Ltd.