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. Before exiting to the outer space, the Helium vapour will cool 3 internal shields between 30 K and 62 K, the external vacuum vessel and the telescope being passively cooled at 80 K. A complex cryostat aperture protected by a radiated baffle will insure the proper propagation of the light from the telescope to the instruments.Two other options have been studied, based on the use of solid Hydrogen and solid Neon.This paper presents AIR LIQUIDE's baseline design together with the rationales for the trade-offs conducted on the thermal and structural point of view.