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This paper deals with a mathematical model of a gas discharge arrester, developed within the Matlab/Simulink program environment on the basis of physical and mathematical parameters. The model includes important physical phenomena regarding a gas discharge arrester, such as its overvoltage causing triggering, discharge processes, electric arc, and a possible repeated dielectric breakdown in gas due to the heat released from the arc to the gas. This paper includes computations for the operating conditions of a gas discharge arrester connected to an ac circuit. The computing results are compared with those measurements of electrical quantities performed on a gas discharge arrester.