Fluid delivery device includes a body, a cannula adapted to extend into subcutaneous tissue, and a septum member adapted to allow a needle to puncture the septum member and to reseal the puncture once the needle is withdrawn from the puncture. The septum member is at least one of a cap-shaped member, a member having at least two non-parallel walls that can each be punctured by a needle, and a member having a generally planar wall and a generally cylindrical wall which can each be punctured by a needle.