The phenomenon of neutron focusing by a totally reflecting conical tube is studied in terms of the focused neutron currents, the spectrum shift, and the gains in beam intensity and in increasing the reaction rate of a 1/v absorber. The influence of the source temperature, the angular spread of the source flux, the geometrical variations of the conical pipe, and the reflectivity are considered. Two different approximate formulations on the focused neutrons in a reflecting tube are established for the purpose of carrying out the numerical calculations. The formulation allows detailed calculations on each order of multiple reflection, taking the tube geometry into consideration. The analysis shows that relatively strongly focused neutron currents are attainable under proper conditions by means of a “focalizer,” a reflecting conical tube. The uses of a multistage focalizer are also suggested, showing examples where both intensity and a 1/v absorption rate in an exposed sample can be enhanced.