Various types of underwater line structures, such as mooring lines, towing lines, flexible risers and oil fences, have been used widely in the ocean. Needless to say, theoretical and/or experimental studies are important to design safe and economical line structures. Many investigations into static and dynamic responses of underwater line structures were made and general-purpose computer programs have been developed using the numerical analysis method, i. e. the finite element method or the lumped mass method. Although, it would be difficult to frequently use these programs because of time and cost savings. At the initial stage of designing the underwater line structures, a more simple method is preferable. In this paper, extensible catenary equations are derived and the fundamental characteristics of catenary are discussed. Next, the ways to solve the equations under various boundary conditions are described. Finally, the examples of its applications are briefly shown.