A disposable safety needle assembly and safety enclosure for internally shielding a used or contaminated needle includes a needle assembly having a needle cannula slidably disposed within a safety enclosure. An angular orientation to the needle within the enclosure maintains an insertion angle allowing the safety enclosure to remain substantially flush with a dermal surface during and while the needle is inserted. The safety enclosure also includes an internally disposed flexible safety member. The flexible safety member has face portion transversely situated and having a safety feature disposed to the needle and that slides thereon. Retracting the needle within the safety enclosure to a point wherein the sharp tip of the needle is beyond the needle protection section of the flexible member causes the protection section to travel transversely to the direction of motion of the needle. As a result, the safety feature receives the sharp tip of the needle.