An MJ-class superconducting magnetic energy storage (SMES) system has a wide range of potential applications in electric power systems. The composite HTS conductor, which has the advantages of carrying large critical currents and withstanding high magnetic fields, is suitable for winding an MJclass magnet coil. However, the Lorentz force of an HTS wire is so large that its induced mechanical stresses should be examined to ensure that the magnet is in good condition. By means of the equivalent material properties method and the sequential coupling method, this paper studies the mechanical properties of a 3 MJ toroidal SMES magnet wound by a composite HTS conductor. Based on the electromagnetic-structural coupling analysis, the Von-Mises stress, the radial stress, and the hoop stress of a magnet coil are calculated and employed to validate the stability of the MJ-class toroidal SMES magnet. Index Terms-SMES, composite HTS conductor, equivalent material properties, sequential coupling, mechanical analysis I. INTRODUCTION UPERCONDUCTING Magnetic Energy Storage (SMES) systems have the advantages of high power density and a fast response speed. They can be used to compensate voltage sags and mitigate power fluctuations in an electrical grid [1]. SMES technology can also be used to facilitate the gridconnection of renewable energy, increase the stability of a power grid and the quality of power supply [2]. In the near future, an MJ-class SMES system is expected to play an important role in power grids. An MJ-class SMES system carries large currents and creates a high field in operation. An SMES magnet is considered to be a key component of the SEMS system. If an SMES magnet were wound by a commercial superconductor, such as a YBCO tape with the cross-section of 4.4 mm×0.1 mm, whose critical current is limited to 100 A~300 A (@77 K, self-field), it would be very difficult to achieve large-capacity energy storage higher than the MJ-class considering the expensive cooling cost. Consequently, it would not provide a favorable condition for the applications of MJ-class SMES systems in power grids. Compared with a parallel stacked wire, a composite HTS