It has been generally known that the chattering of an AC electromagnetic contactor due to the fluctuation of attracting force is the primary cause of its abrasion and noise. To reduce this chattering effect, an AC electromagnetic contactor is mostly fitted with a shading coil which works the role to make difference in phases of two distinct components of attracting force. The theoretical interpretation of an AC electromagnetic contactor with shading coil and the equation of its attracting force per unit wattage consumed have already been proposed, however, few explications so far have been made on the determination of optimal circuit constants of shading coil. In this paper, the auther constructs a circuit model of an AC electromagnetic contactor with shading coil which is based on the theoretical interpretation of shading coil examined to be valid by experiments under some assumptions, and defines the equation of attracting force without chattering per unit wattage consumed as a performance function for determining the optimal circuit constants of shading coil. And then, the optimal circuit constants maximizing the performance function are determined by means of computer simulation founded on the above circuit model and the characteristics of those circuit constants are examined with special attention to the coupling coefficient.