A syringe comprising a syringe barrel, a plunger rod and a stopper attached with the plunger rod within the syringe barrel, said stopper comprising: (a) a main body defining an open rearward end and a closed front end, said open rearward end adapted to receive a front forward end attachment portion of said plunger rod, said main body including an inner surface; (b) a core member integrally formed with said main body adjacent said closed front end, said core member (32, 342) including a nose portion having a conical tip configured for entering an outlet opening of the syringe barrel, said core member including a center post protruding from an interior of the core member toward the open rearward end, said center post including a back core portion adapted for contact with said front forward end attachment portion of the plunger rod; and (c) at least a first rib extending radially outward around a perimeter of said main body, characterized in that said closed front end has a first slope extending from the nose portion (34, 344) to the first rib and wherein the syringe barrel includes a taper extending from the outlet opening of the syringe barrel to a top sidewall portion of the syringe barrel, said taper having a second slope and wherein the first slope is steeper than the second slope, said stopper further comprises (d) a taper provided on said inner surface of said main body, said taper adapted for contact with a corresponding taper on the front forward end attachment portion of the plunger rod, such that application of a forward force to the plunger rod causes said contacting tapers (353, 354) on said stopper and plunger rod respectively to cooperate together to cause at least the first rib of the stopper to apply a radial force "A" to the syringe barrel while a gap is formed between the bottom surface of the center post and the front forward end attachment portion, and application of an increased force to the plunger rod, causes a force "B" to be applied to the conical tip through the center post of the core member as the gap clases which causes the conical tip of the stopper to enter into the outlet opening to result in essentially zero reflux. (a) a main body defining an open rearward end and a closed front end, said open rearward end adapted to receive a front forward end attachment portion of said plunger rod, said main body including an inner surface; (b) a core member integrally formed with said main body adjacent said closed front end, said core member (32, 342) including a nose portion having a conical tip configured for entering an outlet opening of the syringe barrel, said core member including a center post protruding from an interior of the core member toward the open rearward end, said center post including a back core portion adapted for contact with said front forward end attachment portion of the plunger rod; and (c) at least a first rib extending radially outward around a perimeter of said main body, characterized in that said closed front end has a first slope extending from the nose portion (34, 344) to the first rib and wherein the syringe barrel includes a taper extending from the outlet opening of the syringe barrel to a top sidewall portion of the syringe barrel, said taper having a second slope and wherein the first slope is steeper than the second slope, said stopper further comprises (d) a taper provided on said inner surface of said main body, said taper adapted for contact with a corresponding taper on the front forward end attachment portion of the plunger rod, such that application of a forward force to the plunger rod causes said contacting tapers (353, 354) on said stopper and plunger rod respectively to cooperate together to cause at least the first rib of the stopper to apply a radial force "A" to the syringe barrel while a gap is formed between the bottom surface of the center post and the front forward end attachment portion, and application of an increased force to the plunger rod, causes a force "B" to be applied to the conical tip through the center post of the core member as the gap clases which causes the conical tip of the stopper to enter into the outlet opening to result in essentially zero reflux.