The article presents an originally developed mathematical model intended for researching the distribution of currents in a three-phase cable line composed of single-core cables with a rigid dielectric, under the conditions of the occurrence of a short circuit in one of the cables of the respective line. A three-phase calculation procedure, a method of superposition of the state of the stationary drive and a fictitious system, and a quasi-static treatment were applied. Based on the developed mathematical model, the KAUKS program system for the digital computer was created. The KAUKS system was used in the investigation of the current state in the 110 kV cable line, composed of single-core cables of the SIPRELEC type, during the occurrence of a short circuit in one of the cables.