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Auxetic materials are gaining practical interest for their unusual and sometimes extreme mechanical response. The process of modeling these materials so far has highlighted a number of microstructural properties that are key to these materials. However these models often rely on the assumption of homogeneity and order within the materials. Practically, a homogeneous auxetic material such as foam is unlikely to be manufactured. This work seeks to analyze the effect of fluctuations within the microstructure of the material. Numerical results show the effect of fluctuations in an auxetic granular substance and analytical work indicates the relation between microscale fluctuations and the elastic moduli for a general auxetic material. © 2003 American Institute of Physics.