Many of the offshore structures used for oil exploration and exploitation are built of tubular members. The repeated damages in tubular joints have clearly shown that the safety of these structures depends on the safe fatigue design of the joints. The fatigue life of the joint depends very much on the Stress Concentration Factor, SCF. The current practice is to use semi-empirical formulas proposed by various investigators to determine SCF. While some of the formulas give the maximum SCF, others give the SCFs at both the crown and saddle points. The design of fatigue life using the value of maximum SCF is conservative, while using SCFs at crown and saddle is unsafe. The main aim of this paper is to propose a set of formulas for T and Y-joints, which gives not only the magnitude of maximum SCF as in the presently available formulas, but also the variation of SCF around intersection. © 1988 by ASME.