An assembly method for a cross shaft universal joint that comprises: a yoke (7a, 7b) comprising a pair of joining-arm sections(10, 10a, 10b), and a pair of circular holes (15, 15a, 15b) formed in tip-end sections of the pair of joining-arm sections(10, 10a, 10b); a cross shaft comprising a shaft section(17a; 17b); and a pair of cup bearings (18, 18a, 18b) for supporting both end sections of the shaft section (17a, 17b) on an inside of the pair of circular holes (15, 15a, 15b) so as to rotate freely; and the assembly method assembling the pair of cup bearings (18, 18a, 18b) in portions between the pair of circular holes(15, 15a, 15b) of the pair of joining arm sections (10, 10a, 10b) and the both end sections of the shaft section (17a, 17b) that are inserted inside the pair of circular holes (15, 15a, 15b) from the inside-surface sides of the pair of joining-arm sections (10, 10a, 10b) by press-fitting the cup bearings (18, 18a, 18b) inside the pair of circular holes (15, 15a, 15b) from the outside-surface sides of the pair of joining-arm sections (10, 10a, 10b) using a pair of press-fitting punches(33, 33a, 33b); wherein the method comprises a step of adjusting an amount of movement of the pair of press-fitting punches (33, 33a, 33b) according to dimensions of the yoke (7a, 7b) or cross shaft or size of elastic deformation of the pair of joining-arm sections (10, 10a, 10b) during the press-fitting work of the pair of cup bearings (18, 18a, 18b) inside the pair of circular holes (15, 15a, 15b); characterized in that in a state of the pair of joining-arm sections (10, 10a, 10b) being backed up, and the shaft section (17a, 17b) being inserted into the pair of circular holes (15, 15a, 15b) from the inside-surface sides of the pair of joining- arm sections(10, 10a, 10b), one of the pair of cup bearings (18, 18a, 18b) is press-fitted to a preset reference position on the inside of one of the pair of circular holes (15, 15a, 15b), and at that instant, a value of pressure that is applied to one of the pair of press-fitting punches (33, 33a, 33b) is set as a reference pressure; the one of the pair of cup bearings (18, 18a, 18b) is then further press-fitted from the reference position, and at the instant that the pressure applied to the one press-fitting punch (33, 33a, 33b) becomes larger than the reference pressure by a preset value, the one of the cup bearings (18, 18a, 18b) is determined to have reached a position where press-fitting is complete, and the work of press-fitting the one of the pair of cup bearings (18, 18a, 18b) ends. a yoke (7a, 7b) comprising a pair of joining-arm sections(10, 10a, 10b), and a pair of circular holes (15, 15a, 15b) formed in tip-end sections of the pair of joining-arm sections(10, 10a, 10b); a cross shaft comprising a shaft section(17a; 17b); and a pair of cup bearings (18, 18a, 18b) for supporting both end sections of the shaft section (17a, 17b) on an inside of the pair of circular holes (15, 15a, 15b) so as to rotate freely; and the assembly method assembling the pair of cup bearings (18, 18a, 18b) in portions between the pair of circular holes(15, 15a, 15b) of the pair of joining arm sections (10, 10a, 10b) and the both end sections of the shaft section (17a, 17b) that are inserted inside the pair of circular holes (15, 15a, 15b) from the inside-surface sides of the pair of joining-arm sections (10, 10a, 10b) by press-fitting the cup bearings (18, 18a, 18b) inside the pair of circular holes (15, 15a, 15b) from the outside-surface sides of the pair of joining-arm sections (10, 10a, 10b) using a pair of press-fitting punches(33, 33a, 33b); wherein the method comprises a step of adjusting an amount of movement of the pair of press-fitting punches (33, 33a, 33b) according to dimensions of the yoke (7a, 7b) or cross shaft or size of elastic deformation of the pair of joining-arm sections (10, 10a, 10b) during the press-fitting work of the pair of cup bearings (18, 18a, 18b) inside the pair of circular holes (15, 15a, 15b); characterized in that in a state of the pair of joining-arm sections (10, 10a, 10b) being backed up, and the shaft section (17a, 17b) being inserted into the pair of circular holes (15, 15a, 15b) from the inside-surface sides of the pair of joining- arm sections(10, 10a, 10b), one of the pair of cup bearings (18, 18a, 18b) is press-fitted to a preset reference position on the inside of one of the pair of circular holes (15, 15a, 15b), and at that instant, a value of pressure that is applied to one of the pair of press-fitting punches (33, 33a, 33b) is set as a reference pressure; the one of the pair of cup bearings (18, 18a, 18b) is then further press-fitted from the reference position, and at the instant that the pressure applied to the one press-fitting punch (33, 33a, 33b) becomes larger than the reference pressure by a preset value, the one of the cup bearings (18, 18a, 18b) is determined to have reached a position where press-fitting is complete, and the work of press-fitting the one of the pair of cup bearings (18, 18a, 18b) ends.