A high pressure discharge lamp includes a quartz glass bulb, a conductive element which is sealed at a sealing portion of the bulb, and a pair of electrodes. Each electrode is disposed in the quartz glass bulb so as to be opposite the other and connected to the conductive element. A part of each electrode is sealed with the quartz glass bulb at the sealing portion so as to generate a contacting portion formed by the part of each electrode and the bulb. The maximum length, Lmax, of the contacting portion is defined as: Lmax (mm)≦200/(P×D); and the minimum length, Lmin, of the contacting portion is defined as: Lmin (mm)≧0.8/(D2×&pgr;) or Lmin (mm)≧0.7 whichever is longer, where D is the diameter (mm) of the electrode and P is the power (W) supplied to the electrode.