Abstract: A threaded connection for improving fatigue resistance to cyclic loading is disclosed. The threaded connection basically comprises a pair of interlocking members having corresponding radially inner and radially outer spiral threads thereon, each spiral thread including a spiral compression flank and a spiral tension flank wherein at least one of the spiral compression flanks and spiral tension flanks on the inner spiral threads are in mating planar engagement with a corresponding spiral compression flank and spiral tension flank on the outer spiral thread. Axial spacing between the tension flanks and the compression flanks on the radially inner and radially outer spiral threads further define a stress reducing spiral root surface on at least one of the radially inner and radially outer threads and a corresponding crest surface on the other radially inner and radially outer spiral threads.