In this thesis, an efficient and accurate drug assay system in a microfluidic device was developed, considering the $\It{in vivo}$ delivery path of drugs in humans. Among the various drug assays, drug permeability assays in the intestine and brain, and hepatotoxicity assay in the liver are very important for drug screening and development process. The microfluidic assay system for drug permeability and hepatotoxicity assays using a cell trapping method reduces the assay time as no cell culture in the microfludic device is required and no complex structure, such as cellular membrane, is needed. The microhole array for cell trapping was fabricated using the poly(dimethylsiloxane) (PDMS) molding technique for mimicking the intestinal epithelial cell membrane. Based on mathematical simulations, the configuration of the microfluidic device, including a microhole array and a mixing channel, and the flow rate were optimized to trap cells firmly in each microhole without cell damage. The permeability of ten drugs was measured and compared with the reported values of permeability in the human and rat intestine. On the other hand, drug transportation from blood to brain is restricted by the specialized membrane of brain capillary endothelial walls, namely blood brain barrier (BBB). With the same device, a permeability assay system was also performed using human umbilical vein endothelial cells (HUVECs) trapped in microholes, with or without astrocyte conditioned medium (ACM) in a microfluidic device. From the permeability assays of five widely used drugs for measuring BBB permeability, the measured permeability values were highly correlated with the permeability value of $\It{in vitro}$ BBB model and brain uptake index (BUI). Hepatocytes have been used for $\It{in vitro}$ hepatotoxicity assays because of their ability to sustain intact liver-specific function. In order to investigate drug effects on hepatic function using primary human hepatocytes, hepatotoxicity assays ...