Neutron transmission in various materials promising for the manufacturing of neutron filters based on single-crystalline and polycrystalline bismuth and sapphire single crystals is studied. Experimental results show that for neutrons with wavelengths of λ > 2.5 Å the transmission coefficient attains ∼88% for bismuth and ∼78% for sapphire single crystals. At the same time, the maximum transmission for polycrystalline bismuth does not exceed ∼18%. The possibility of manufacturing X-ray filters for neutron beams based on single-crystalline bismuth and sapphire is discussed.