We present a study of elemental abundances in a sample of thirteen Blue Compact Dwarf (BCD) galaxies, using the $sim$10--37$mu$m high resolution spectra obtained with Spitzer/IRS. We derive the abundances of neon and sulfur for our sample using the infrared fine-structure lines probing regions which may be obscured by dust in the optical and compare our results with similar infrared studies of starburst galaxies from ISO. We find a good correlation between the neon and sulfur abundances, though sulfur is under-abundant relative to neon with respect to the solar value. A comparison of the elemental abundances (neon, sulfur) measured from the infrared data with those derived from the optical (neon, sulfur, oxygen) studies reveals a good overall agreement for sulfur, while the infrared derived neon abundances are slightly higher than the optical values. This indicates that either the metallicities of dust enshrouded regions in BCDs are similar to the optically accessible regions, or that if they are different they do not contribute substantially to the total infrared emission of the host galaxy.