In a high pressure discharge lamp having electrode rods with grooves formed in a part thereof and embedded and sealed in sealing parts of a discharge vessel, breakage of the sealing parts because of the grooves is prevented without impairing the mechanical strength of the electrode rods, in which the grooves are formed, by the high pressure discharge lamp comprising: a discharge vessel having a light emitting part and sealing parts connected to both ends of said light emitting part; and electrodes comprising electrode rods and electrode tip end parts arranged oppositely to each other in the light emitting part, said electrode rods being embedded in a respective one of said sealing parts, and axially directed grooves being formed in at least part of the surface of said electrode rods, wherein a diameter measured at groove bottom parts of the grooves of said electrode rods is larger than a diameter of the electrode rods in a part where no grooves are formed.