Some embodiments of a medical infusion pump system include a pump device having a flexible pushrod that can adjust from a curved configuration to a generally straight configuration. The flexible pushrod is part of a drive system of the pump device so that the flexible pushrod can be controllably and incrementally advanced toward a medicine reservoir to incrementally dispense the medicine therein. In particular embodiments, the flexible pushrod may comprise an anti-rotation mechanism, an anti-torsion mechanism, or a combination thereof.