Multilayer Mo/Be/Si mirrors with different ratios of Si- and Be-layer thicknesses in a period are considered. It is shown that the substitution of silicon with beryllium in the Mo/Si system makes it possible to completely eliminate internal stresses in the Mo/Be/Si structure. Layer thicknesses are found (Si similar to 0.9 nm, Mo similar to 2.8 nm, and Be similar to 3.3 nm) that simultaneously provide high reflection coefficients (R similar to 66-67%) at a wavelength of 13.5 nm and zero values of internal stresses.