An I.V. flush syringe (20) assembly includes a barrel (22) having an inside surface (32) defining a chamber (33) for retaining fluid, an open proximal end (28) and a distal end (30) including a distal wall (31) with an elongate tip (36) extending distally therefrom having a passageway (38) therethrough in fluid communication with the chamber (33). A plunger (24) having an elongate body portion (25) and a stopper (54) slidably positioned in fluid-tight engagement with the inside surface (32) of the barrel (22) is provided. Anti-reflux structure for controlling stopper deflection when fluid has been delivered from the chamber (33) and the stopper (54) is in contact with the distal wall (31) is provided. The anti-reflux structure includes the stopper (54) having a conically shaped distal surface (59) and the inside surface (32) of the barrel (22) and the distal wall (31) being conically shaped (35) wherein the total included angle A of the inside surface (32) of the barrel (22) at the distal wall (31) is greater than the total included angle B of the distal surface (59) of the stopper (54) by at least 6°.