The transport phenomena in a bioartificial liver (BAL) were investigated experimentally from a viewpoint of fluid mechanics. BAL used in this study was a type of utilizing a hollow-fiber dialyzer. The suspension of hepatocytes was packed in the lumens and the blood was fed into the shell side. In the BAL, the permeation rate of the substances in the blood including oxygen is one of the most important factors for the evaluation of the performance. It has been considered that the permeation is driven by concentration difference between the lumen and the shell side. According to the increase of the permeability of the membrane, the permeation driven by the transmembrane pressure (TMP) is expected to become dominant. In this study, the axial pressure distributions in the shell side were measured. Water suspension of starch powder used as a model of the suspension of hepatocytes was injected into lumens. On the other hand, an aqueous solution of glycerol was fed into the shell side instead of blood. Based on the results, it was confirmed that the permeation driven by TMP occurred. In addition, the importance of the permeation was discussed.