1. A safety hypodermic syringe (1) comprises a barrel (3) having a plunger operated piston therein and a hollow spigot (11) extending from one end (7) of the barrel (3) and connected to the interior of the barrel (3) An hollow needle (13) is detachably attached to the spigot (11) by means of a cup portion (15) at the end of the needle (13) away from the point (18), the spigot (11) having a reduced diameter portion at its distal end for receipt of the needle cup portion (15) so that the cup portion (15) lies substantially flush with the remainder of the spigot (11). A cap (31) is detachably fitted to the said one end (7) of the barrel (3) so as to cover the needle (13). The cap (31) has a length (L) measured from the inner end (16) of the needle (13) adjacent to the needle cup portion (15) to the opposite end of the cap (31), which is at least twice the length (I) of the needle (13) being the length of the needle (13) beyond the cup portion (15) and or the inner diameter (D) of the cap (31) is at least one sixth larger than the outer diameter (d) of the needle cup portion (15).