The stress-strain state for thin beryllium windows of circular shape under cyclic loading by external pressure was calculated using finite element method. The technique for estimating the beryllium window’s fracture probability was proposed. Technique is to compare the accumulated plastic strain in a foil with a certain value of the critical plastic strain, determined experimentally by foil samples bending tests. An experimental study of the durability for beryllium windows with a thickness of 8 μm under cyclic loading with external pressure was performed. Good convergence between the predicted and the fact number of load cycles without fracture was established.