Abstract: A high pressure discharge lamp 1A has a light emitting vessel 2A made of a semitransparent ceramic material and having a pair of end portions 2a each with an opening formed in the end portion and a light emitting portion 2a, a pair of discharge electrodes 5, and electrode supporting members 4 each supporting the electrode 5 and fixed to the end portion 2a. The vessel 2A defines an inner space 6 with an ionizable light emitting substance and starter gas filled in the inner space 6. The electrodes 5 are contained in the inner space 6. The light emitting portion 2b has a thicker portion 2g and a thinner portion 2c. The thinner portion 2c has a cross sectional area of not smaller than 35 percent and not larger than 80 percent of that of the thicker portion 2g so that the light emitting portion 2b has a brightness center 9 in the thinner portion 2c.