Vacuum-tight windows can be used to isolate an ultrahigh vacuum (UHV) synchrotron beamline from the equipment of an experimenter operating in a non-UHV environment. A thin beryllium plate mounted on a vacuum flange can be used as a high transmission window/filter for experimenters using synchrotron radiation in the X-ray region. Synchrotron radiation absorbed in the center of a beryllium window is converted to heat. This paper investigates the mechanical and thermal stresses in a beryllium window when that window is used as both a vacuum seal and a synchrotron radiation filter. Thermal and mechanical stresses are calculated using ANSYS - a finite element engineering analysis program which allows inclusion of nonlinear stress factors.