Experimental infrared resonance absorption line profiles are compared with results from T-matrix theory calculations for several mineral components of atmospheric dust (illite, kaolinite, montmorillonite, quartz, and calcite). The model results are used to infer general characteristics of the aerosol particle shape distribution. For the silicate clays the spectral line profiles are best fit by a shape distribution of highly eccentric oblate spheroids, consistent with the expected sheet-like nature of the clay minerals. For quartz dust the spectral line profiles are best fit by a very broad distribution including both extreme oblate and prolate spheroids. For calcite a spheroid model with moderate shape parameters gives the best fit. Our results suggest that high-resolution IR extinction measurements may offer useful insight into the shape distributions of atmospheric mineral dust.