Marine riser conduit section coupling means adapted to withstand high riser tension and bending loads in deep sub sea well drilling and production operations by preventing stress concentrations has upper and lower coupling members, each being mounted to an associated marine conduit section, and fastening means for securing the coupling members together wherein the outer surface configuration for each said coupling member comprises an effectively continuous arcuate surface extending circumferentially about substantially the entire outer surface of each coupling member from one axial extremity thereof adjacent the associated conduit section to an opposite extremity thereof adjacent outer marginal areas of the associated member flange. The fastening means include threaded bolts and means for preventing their inadvertent removal from a connector flange when disconnected from the mating flange.A preferred outer surface configuration for each coupling member is substantially a quarter of an ellipse whose major axis is parallel to the bore of the riser, and said major axis being approximately twice the length of the minor axis.