A system for cryogenic vitrification of a substance, said substance comprising biological material to preserve, such as an embryo or an oocyte, and received in a packaging casing, said casing comprising a thin tube of predetermined dimensions having an opening at a first end and being closed off in the neighborhood of a second end which is an opposite end to said first end, said casing forming part of a packaging set for said substance comprising, in addition to said casing, a receiving carrier configured to receive a predetermined volume of said substance and to be inserted inside said thin tube such that said predetermined volume of said substance is located in a receiving region of said thin tube located at a distance from said opening of said thin tube; said system comprising a tub configured to contain a bath of a cryogenic agent and at least one carrier member configured to hold said thin tube in a predetermined orientation and to be mounted on said tub in a first predetermined position in which said thin tube is uprightly oriented in said tub, said receiving region of said thin tube is immersed in a liquid zone of said bath of cryogenic agent where said cryogenic agent is in the liquid state, and said opening of said thin tube is located above said bath of cryogenic agent, in a zone of ambient air surmounting said bath of cryogenic agent, to enable the insertion of said receiving carrier of said substance into said thin tube; said system being characterized in that said carrier member is configured to be mounted on said tub in at least one second predetermined position, lower than said first predetermined position, in which second predetermined position said thin tube is uprightly oriented in said tub, said receiving region of said thin tube is immersed in said liquid zone, and said opening of said thin tube is located immediately above said liquid zone, in a gaseous zone of said bath of cryogenic agent, surmounting said liquid zone and where said cryogenic agent is in the gaseous state, and below said ambient air zone surmounting said bath of cryogenic agent, and to be raised from said second predetermined position to said first predetermined position. said system comprising a tub configured to contain a bath of a cryogenic agent and at least one carrier member configured to hold said thin tube in a predetermined orientation and to be mounted on said tub in a first predetermined position in which said thin tube is uprightly oriented in said tub, said receiving region of said thin tube is immersed in a liquid zone of said bath of cryogenic agent where said cryogenic agent is in the liquid state, and said opening of said thin tube is located above said bath of cryogenic agent, in a zone of ambient air surmounting said bath of cryogenic agent, to enable the insertion of said receiving carrier of said substance into said thin tube; said system being characterized in that said carrier member is configured to be mounted on said tub in at least one second predetermined position, lower than said first predetermined position, in which second predetermined position said thin tube is uprightly oriented in said tub, said receiving region of said thin tube is immersed in said liquid zone, and said opening of said thin tube is located immediately above said liquid zone, in a gaseous zone of said bath of cryogenic agent, surmounting said liquid zone and where said cryogenic agent is in the gaseous state, and below said ambient air zone surmounting said bath of cryogenic agent, and to be raised from said second predetermined position to said first predetermined position.