A general thermodn. equation for the swelling of a crosslinked polymer system in the vapor of a swelling agent has been derived under isothermal and isobaric conditions. The equation is used to describe the equil. uptake of water by Arnitel elastomers, which are hard-soft-segment block copolymers in which the hard segments, poly(butylene terephthalate), crystallize and are responsible for a phys. crosslinking. The gravimetrically detd. degrees of swelling of different elastomers in water vapor of various partial pressures are analyzed and discussed by the application of an extended semi-empirical swelling equation of Flory-Huggins-Staverman-van Santen.