The container (11) includes a side wall (15) defining a syringe storage chamber (19) where a coiled strip pack (31) of syringes (29) is placed. A central core (35) is place concentrically within the container and forms a collection chamber (20) for used syringes. The side wall (15) includes an outlet opening (30) so that the strip pack (31) can be paid out through the opening (30) and the syringes can be dispensed. The used syringes (29) will be pushed, needle-first through the central opening (26) and into the collection chamber (20), whereby when all the syringes in the strip pack are used and deposited into the collection chamber, the entire container can be disposed of, as by burning.