The collapse failure of rock surrounding caverns involves a progressive collapse process. Based on the nonlinear Hoek–Brown failure criterion and the upper limit theorem, the whole process curve of the progressive collapse of the surrounding rock of a large-span cavern is outlined in this paper. The progressive collapse process of the surrounding rock of the large-span cavern is experimentally studied using an independently developed visualized large-span-cavern geomechanical model test device with variable angles. The results show that, through theoretical calculation and model tests, the surrounding rock at the top of the large-span cavern undergoes three collapses. Under the condition of rock mass and the shape of the cavern, the larger the span of the cavern, the more times the surrounding rock collapses; with the increase in surrounding rock pressure, the first collapse occurs in the middle part of the arch roof. When the overlying load reaches a certain level, the arch foot becomes the weakest part, and the rock undergoes shear failure along the arch foot, gradually extending upwards, accompanied by multiple collapses, forming a progressive collapse process. The theoretical calculation results of this paper are basically consistent with the scope of the model test, and the research results can provide a basis for the construction and support design of the large-span cavern.