Abstract: An offshore riser includes a plurality of tubular elements, each having a pin member on one end and a box member on the other end for connection with adjacent tubular elements. The pin member has an external thread which engages an internal thread on the box member of the adjacent tubular element. A dual angle torque shoulder locks the box end securely into place against the pin, preventing radial distention of the box end and maintaining bearing pressure between the external sealing surfaces. Also, stress relief grooves are located on the box member and on the pin member, to reduce the incidence of stress fractures, thereby improving the fatigue life of the connection.