Hydrodynamic chromatography (HDC) is a well-established analytical separation method for the size separation of nano- and microparticles and large molecular weight solutes such as synthetic polymers and proteins. We report on a theoretical study showing that the separation resolution of open-tubular HDC can be significantly enhanced by changing the cross-sectional shape of the separation channel. By enforcing Brenner's macro-transport approach, we provide theoretical/numerical evidence showing how the shape of the cross section influences quantitatively both the selectivity and the axial dispersion of the suspended particles in HDC. The separation performance of square-, triangle-, and star-shaped channel cross sections is compared to that of a cylindrical capillary over three decades of the particle Péclet number in terms of the minimal separation length and time to obtain the unit resolution of a two-particle mixture. Enhancement factors up to 400% are found in the case of triangular shapes, with the best performing case being the 70.6° angle, which can be obtained by KOH etching of bulk silicon.