We have measured the mechanical strain, θ = d L θ L θ , using strain gauges adhered along the circumferential (θ) direction on the EuBaCuO ring bulk reinforced by an aluminum alloy ring during the cooling process from 289 K to 50 K, and during field-cooled magnetization (FCM) at 50 K under magnetic fields from Bapp = 5.3 and 6.3 T. To discuss the mechanical reinforcement effect of the aluminum alloy ring and the magnetic strain during FCM, we have performed numerical simulations using the finite element method for the ring bulk assuming realistic superconducting characteristics. The experimental results of the thermal strain during the cooling process, θ c o o l = d L θ c o o l L θ , from 289 K to 50 K on the bulk surface validated our numerical results, in which the θ c o o l value became smaller at the outer edge, compared to that at the inner edge of the bulk surface. These results strongly suggest an inhomogeneous reinforcement of the bulk due to the difference in the thermal contraction along the height direction between the ring bulk and the outer Al alloy ring with finite height. The experimental results of the time step dependence of the magnetic strain during FCM, θ F C M = d L θ F C M L θ , were reproduced qualitatively by the numerical simulation. The measurement of mechanical strain is effective to clarify the reinforcement effect of the metal ring during cooling and the mechanical stress during FCM.