A method for producing a high pressure discharge lamp including a luminous bulb enclosing a luminous substance inside and a sealing portion for retaining airtightness of the luminous bulb, includes preparing a glass pipe for a discharge lamp including a luminous bulb portion that will be formed into a luminous bulb of a high pressure discharge lamp and a side tube portion extending from the luminous bulb portion; inserting a glass member constituted by a second glass having a softening point lower than that of a first glass constituting the side tube portion into the side tube portion, and then heating the side tube portion so as to attach the glass member and the side tube portion; and after the attachment step, heating a portion including at least the glass member and the side tube portion at a temperature higher than a strain point temperature of the second glass and lower than a strain point temperature of the first glass.