This paper presents a method of computer simulation useful for analysis of an axially symmetrical magnetic circuit with exciting coils, magnetic poles, and permanent magnets. The vector magnetic potential is obtained by the use of the well-known successive over-relaxation method, so that devices having magnetic hysteresis characteristics can be analyzed easily and accurately. In this program, the magnetization intensity distribution within the magnet is taken into account. The new computer programming system is applied to a magnetic shielding hollow sphere, a bar magnet, a ring magnet, and a periodic permanent-magnet structure for traveling-wave tubes, and the flux distribution for these magnetic circuits is shown. The results are seen to be in good agreement with theoretical and experimental values.