In recent years a unique drug delivery system named as the transdermal drug delivery system has been developed which can deliver drug particles to the human skin without using any external needle. The solid drug particles are accelerated by means of high speed gas flow through a shock tube imparting enough momentum so that particles can penetrate through the outer layer of the skin. Different systems have been tried and tested in order to make it more convenient for clinical use. One of them is the contoured shock tube system (CST). The contoured shock tube consists of a classical shock tube connected with a correctly expanded supersonic nozzle. A set of bursting membrane are placed upstream of the nozzle section which retains the drug particle as well as initiates the gas flow (act as a diaphragm in a shock tube). The key feature of the CST system is it can deliver particles with a controllable velocity and spatial distribution. The flow dynamics of the contoured shock tube is analyzed numerically using computational fluid dynamics (CFD). To validate the numerical approach pressure histories in different sections on the CST are compared with the experimental results. The key features of the flow field have been studied and analyzed in details. To investigate the performance of the CST system flow behavior through the shock tube under different operating conditions are also observed.