In connection with the design and construction of transmission lines in the mountainous Appalachian region the writers have evolved a method of making mathematically exact sag and tension calculations based on catenary formulas that eliminates the trial and error assumptions involved in a portion of the Martin method. The working formulas used by the writers require only simple arithmetical calculations which can be handled by clerical personnel usually available in the engineering office. The calculations are not laborious, and can be easily checked. The writers' method not only develops the sags, tensions, and conductor lengths for the various final and initial conditions of the design span (basic or ruling span), but also similar data for span lengths other than the ruling span. The procedure outlined is applicable to any cable or wire whose modulus of elasticity and coefficient of expansion are uniform throughout the cross section, such as is the case with copper, copper-coatedsteel, or steel cables. Sag and tension problems for composite cables such as aluminum cables steel reinforced, are usually solved by graphic methods based on stress-strain curves developed from laboratory tests on the particular cable under consideration. The writers' method does, however, develop previously unpublished relationships between sags, tensions, and cable lengths which are applicable not only to copper, copper-coated-steel, and steel cables, but also to problems involving composite cables, which information cannot be secured by graphic methods alone. The text gives the basic catenary formulas, the derivations thereof, and an explanation of the procedure followed in actual sag calculations.