Clinical studies suggest that the flow of bile in the biliary system may be a contributing factor in the pathogenesis of cholelithiasis, but little is known about its transport mechanism. This paper reports a numerical study of steady flow in human cystic duct models. In order to obtain parametric data on the effects of various anatomical features in the cystic duct, idealised models were constructed, first with staggered baffles in a channel to represent the valves of Heister and lumen. The qualitative consistency of these findings are validated by modelling two of the real cystic ducts obtained from operative cholangiograms. Three-dimensional (3D) models were also constructed to further verify the two-dimensional (2D) results. It was found that the most significant geometric parameter affecting resistance is the baffle clearance (lumen size), followed by the number of baffles (number of folds in the valves of Heister), whilst the least significant ones are the curvature of the cystic duct and the angle between the neck and the gallbladder. The study presented here forms part of a larger project to understand the functions of the human cystic duct, especially the influence of its various anatomical structures on the resistance to bile flow, so that it may aid the assessment of the risk of stone formation in the gallbladder.