It is an X-ray generating apparatus having an X-ray shielding means superior in thermal conductivity. The X-ray generating apparatus comprises an X-ray tube, an X-ray tube container, and a support member which is constructed of an electrically insulating material and which supports the X-ray tube within the X-ray tube container, the X-ray tube container being constituted by a combination of copper alloy plates with lead incorporated therein and a plate of a composite material, the composite material being formed by laminating lead and epoxy laminated glass cloth sheets so as to include an intermediate layer of lead, the X-ray tube container having an aperture (for X-ray emission and containing the X-ray tube so as to prevent the emission of X-ray from any other portion than the aperture.