The AutoSyringe is an automatic device that allows patients with limited dexterity to administer medication to themselves as painlessly as possible. The device allows patients to inject themselves subcutaneously, where the needle goes into the fat layer between the outer skin and the muscle. In this study, given a constant pressure applied at the plunger, the flow of medication through the barrel and needle of a syringe was modeled in terms of velocity and pressure. Furthermore, through this model it was found that the flow rate at the tip of the needle decreases with increased viscosity of the medication. It was also determined that the flow rate increases with increased applied pressure at the plunger. These analyses were performed using the software package FIDAP, PreSTO, with imported geometry from GAMBIT.