In this paper, we propose an effective mechanical reinforcement of a REBaCuO superconducting disk bulk pair to avoid mechanical fracture due to a large hoop stress during field-cooled magnetization (FCM), and confirm the reinforcement effect using numerical simulation. In this reinforcement, the disk bulk is fully encapsulated by an outer metal ring with upper and lower plates made by stainless steel (SUS316). The trapped field, B z , in the bulk pair with various critical current densities, J c , was numerically simulated during FCM from B app =22 T, and the hoop stress, σ θ , was also estimated during FCM after cooling from 300 to 20 K. As a result, the trapped field of over 20 T can be achieved in the gap center of the bulk pair. A large compressive hoop stress, s q , cool due to the difference of thermal expansion coefficients between the bulk and stainless steel, was effectively applied to the whole bulk during the cooling process, compared to that for the conventional reinforcement using only a SUS316 outer ring. The electromagnetic hoop stress, σ θ FCM , during FCM was also reduced, and the maximum of the total hoop stress, s q total (=σ θ FCM +s q cool), can be reduced below the fracture strength of the REBaCuO bulk. The possibility to achieve a higher trapped field over 20 T is suggested in the gap of the REBaCuO bulk pair without mechanical fracture.