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FIRST, a European Space Agency (ESA) program, is a multi-user observatory covering the wavelength range from 80 µm to 670 µm. It is the successor of the Infrared Space Observatory (ISO). FIRST will be launched in year 2007 by the ARIANE V launcher together with the PLANCK satellite. It will remain 3.5 years in operation at the second Lagrangian point of the earth - sun system. AIR LIQUIDE / DTA, as contractor of ESA, has performed an alternative study of the complete cryogenic system resulting in the preliminary design of a large Super fluid Helium cryostat at 1.65 K. The cryostat will be composed of an external vacuum vessel supporting the telescope, the sunshield, various external equipment and containing the Helium tank and the instruments. The main HeII tank (2250 litres) will provide cooling power to the three instruments at 1.7 K, 4.3 K and 15 K for a design lifetime of 3.5 years.