A theoretical study is made of the reflection of neutrons by a multilayered conical tube which extends the concept of reflection by a single-layer tube. Such a device is useful for producing an intense neutron beam. Two types of this tube are discussed: One produces a high quality beam of greater intensity than obtainable with a conventional collimator. The study shows that the intensity of the thermal neutron beam is 8 to 30 times as strong as that by simple collimation. The other type is for neutron spot-irradiation and is illustrated by establishing a beam of 6100 n/ (cm2 sec) at a focal point from a source flux of 106 n/ (cm2 sec).