Needle-free jet injection allows delivery of a liquid drug through the skin in the form of a narrow fluid jet traveling at high speed, minimizing the risks of accidents. Doing this in a controlled way requires an actuator with exceptionally high force density. We propose the use of linear permanent magnet fluxswitching motors for this task, and describe their characteristics relative to the needs of jet injection. This paper will introduce a design process which involves the use of artificial neural networks as a means of response surface modelling, combined with nonlinear constraint optimization, to deduce a motor design that satisfies all of the challenging linear motor requirements for needle-free jet injection applications.