In this paper, the trapped field, Bz, thermal hoop stress, σθcool, by cooling from 300 to 50 K and electromagnetic hoop stress, σθFCM, during field cooled magnetization (FCM) from Bapp = 6.3 and 9.4 T are investigated numerically for ring-shaped REBaCuO bulks with various inner diameters (I.D.) and heights (H) and reinforced by an Al alloy ring. For simplicity, an identical critical current density, Jc(B), which is a typical value at 50 K, is assumed in the simulation. The Bz value at the center of the ring bulk changes depending on the I.D. and H values of the ring bulk, which results from the different distribution of the superconducting current. As a result, the total hoop stress, σθtotal, (= σθcool + σθFCM) also changes for each ring bulk and for each Bapp due to the variation of the σθcool and σθFCM values. The maximum σθ total value, which affects the bulk fracture at Bapp = 9.4 T, increases with decreasing the height of ring bulk. These results can present guidelines for designing a trapped-field magnet using ring bulks.