The paper reports the use of three-dimensional creep continuum damage mechanics techniques to study the creep failure of a medium-bore low-alloy ferritic-steel cylinder-cylinder branched pressure vessel welded connection, tested at a constant pressure of 4 MPa, at a uniform temperature of 590 • C. The development of computational techniques is reported to analyse this problem with a four-material model of the welded connection which includes: parent, type IV, heat-affected zone (HAZ) and weld materials. The results of analyses are presented for two sets of creep damage constitutive equations. For both equation sets, lifetimes are conservatively, yet accurately predicted; however, the results of metallographic examinations of a tested vessel are not accurately predicted. To overcome this deficiency further analyses of the vessel are recommended which include: a coarse-grained HAZ (CGHAZ), adjacent to the weld material; and, more-refined finite element modelling.