[en] The Cryogenic Dark Matter Search (CDMS) is an experiment to detect weakly interacting massive particles (WIMPs), which may constitute the universe's dark matter, based on their interactions with Ge and Si nuclei. We report the results of an analysis of data from the first two runs of CDMS at the Soudan Underground Laboratory in terms of spin-dependent WIMP-nucleon interactions on ⁷³Ge and ²⁹Si. These data exclude new regions of WIMP parameter space, including regions relevant to spin-dependent interpretations of the annual modulation signal reported by the DAMA/NaI experiment