Abstract: The stress-strain state and deformation of thin beryllium round-shaped windows are calculated under cyclic loading by external pressure using the finite element method. The possibility of fracture probability estimating by comparing the accumulated plastic strain in a foil with a certain plastic strain limiting (critical) value was shown for beryllium windows. A technique of plastic strain limiting (critical) intensity experimental determination by testing foil samples for bending up to fracture was proposed. Experimental testing of 0.008 mm thick beryllium windows showed a good match of predicted fracture of beryllium foil with experimental data.