A subperiosteal syringe assembly for storing, containing and delivering bone graft material to a location within the tissue of a jaw for use in a medical procedure. The syringe assembly has a lumen body that is maneuverable within the subperiosteal tissue to deposit bone graft material at the desired surgical site. Embodiments include a lumen body that has a flat shape, such as an elliptical shape. A plunger is provided to deliver the syringe contents. The syringe may be loaded with bone graft material, and some embodiments may be supplied pre-loaded with bone graft material. An end cap seals the open end of the lumen, and may function as a septum that may be punctured with a needle to introduce a liquid substance, such as a growth factor, into the lumen where the bone material is stored. The syringe may be designed to incorporate surgical navigation and laparoscopic systems.