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We present a mathematical model of the dynamics of a previously developed needle-free jet injector (NFJI) that is based upon a servo-controlled Lorentz-force motor. The injector creates a fluid jet that can pierce through the skin and deliver a drug to dermal, subcutaneous and muscular tissue. We use the model to predict the jet speed achieved during an injection. The model simulates the electrical response of the motor coil, the mechanical response of the drug piston and ampoule and the friction incident upon the piston during the time course of the injection. High-speed video measurements of piston movement in response to a step input show that the model predicts piston-tip position during an injection within an RMS error of 287 µm. The corresponding jet speed is predicted to be 180 m·s−1 with a maximum overshoot to 205 m·s−1. [ABSTRACT FROM PUBLISHER]