A jet-propelled particle injection system, the biolistics, has been developed and employed to accelerate micro-particles for transdermal drug delivery. We have examined a prototype biolistic device employing a converging-diverging supersonic nozzle (CDSN), and found that the micro-particles were delivered with a wide velocity range (200-800 m/s) and spatial distribution. To provide a controllable system for transdermal drug delivery, we present a contoured shock-tube (CST) concept and its embodiment device. The CST configuration utilizes a quasi-steady, quasi-one dimensional and shock-free supersonic flow to deliver the micro-particles with an almost uniform velocity (the mean velocity and the standard deviation, 699 4.7 m/s) and spatial distribution. The transient gas and particle dynamics in both prototype devices are interrogated with the validated computational fluid dynamics (CFD) approach. The predicted results for static pressure and Mach number histories, gas flow structures, particle velocity distributions and gas-particle interactions are presented and interpreted. The implications for clinical uses are discussed.