A safety device 20 for shielding a medical needle 25 having a sharp tip includes a needle mount 28 which is adapted directly or indirectly to support the needle 25. A needle shielding sleeve 33 is arranged coaxially with the mount 28 for sliding movement between an initial shielding position surrounding the needle 25 and a non-shielding position at which at least the tip of the needle is exposed beyond the sleeve 33. Resilient fingers 35 urge the sleeve 33 to its needle shielding position. There is a control member 39 for the fingers 35 and which is slidably housed within the coaxial arrangement of the sleeve 33 and the mount 28. The resilient fingers 35 are essentially undeformed when the control member 39 is in its storage position (FIG. 3A) but are partially deformed when the control member is moved to a set position (FIG. 5A). A needle cover 42 is fitted on to the needle 25 to confer protection thereto but is removable from the needle prior to use of the device and is arranged so that removing the needle cover effects movement of the control member to its set position.