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Resistance-network analogues have been used experimentally for longitudinal step-by-step solution of the thermal problem in separate-water-pipe cooling of underground e.h.v. cables. In parallel with this technique, mathematical models have been programmed for digital and analogue computers. The feature of the digital solution is the use of two programs; the first need only be run once, giving results which are applicable as boundary conditions to various cable and pipe geometries in the second program, in which both radial and square meshes are used. The analogue program in which the digital results are used is simple, versatile and suitable for general application to most cable geometries. The derivations of the thermal equations and the development of the computer programs are given in detail, and results for typical cable systems are presented.