Cylindrical cryogenic targets are required to carry out the Laboratory Planetary Science scheme of the experiments of the High Energy Density matter Generated by Heavy Ion Beams collaboration at FAIR. In this paper, for the first time a thorough analysis of the problem of such targets' fabrication, delivery and positioning in the center of the experimental chamber has been made. Particular attention is paid to the issue of a specialized cryogenic system creation intended for rep-rate supply of the High Energy Density matter Generated by Heavy Ion Beams experiments with the cylindrical cryogenic targets.
