To deal with the problems of the local stress concentration caused by the internal hydraulic pressure during the operation of cubic press, we have used the theory of thick-wall block to analyze and calculate the loads of the hinge beam block. The results demonstrate that the working block suffering from the excessive hydraulic pressure contacts with the bottom of hinge beam each other, which gives rise to the stress concentration in the arc of the bottom of the hinge beam block. According to the data of the theoretical calculation, the strain tests of the arc are completed by the strain testing methods in the bottom of the hinge beam block. The Comparison between the data of the two groups has verified their consistency. It also confirms the theoretical calculation is reasonable and accurate at the same time.