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A series of feasibility studies were carried out on the applications of a high-temperature superconducting (HTS) coil system for a medical accelerator system for particle cancer therapy by our group. A new HTS cyclotron is designed to be more compact and have higher efficiency than the conventional medical accelerator. High strength against electromagnetic forces is required for the development of compact HTS coils during the use of an HTS cyclotron. A new stress control structure for a high-strength REBCO pancake coil was proposed in the previous study. No deterioration was observed in the double pancake coil after a charging test of 1.5 kA at 4.2 K in 8-T backup fields. The maximum hoop stress was determined to be greater than 1.7 GPa because of the Lorentz force. The developed coil structure was able to share the hoop stress with not only the coil winding but also the reinforcing structures. In this study, numerical structural analysis based on the finite element method was performed on the new coil structure to clarify the mechanism of the stress sharing between the coil winding and reinforcing structures. In addition, the stress sharing effect of the meter-class REBCO coil assuming an HTS cyclotron system was determined.