Improvements in a safety hypodermic needle and a method of making the same are disclosed. The improvements relate to a commercial embodiment of a patented safety needle and comprise a tubular member extruded from a flexible elastomeric or rubber-like polymeric material. The tubular member is extruded with two ribs extending from the outer wall of the tubular member and spaced apart 90° circumferentially. The wall of the tubular member is provided with through cuts to form a cutout on one wall portion and an elongated lever on the opposite wall portion in the 90° space between the ribs. The cuts separate the wall of the tubular member into two outwardly flexible arms, each having a single rib thereon adjacent an edge of the arm. One end of the tubular member is stretched over the needle hub of a hypodermic needle and the other end is stretched over a needle cup which houses the sharp needle point. The needle cup is provided with a needle opening through which the needle extends during use. After use the flexible arms automatically return the needle cup into a protective position housing the needle point. Latching mechanisms are provided on the hub and lever for releasably holding the arms in a “cocked” position or for permanently holding the arms in a disabled or “safe” condition to prevent inadvertent needle sticks.