We present a study of elemental abundances in a sample of 13 blue compact dwarf (BCD) galaxies, using the ∼10-37 µm 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, although sulfur is underabundant relative to neon with respect to the solar value. A comparison of the elemental abundances (neon and sulfur) measured from the infrared data with those derived from the optical (neon, sulfur, and oxygen) studies reveals a good overall agreement for sulfur, while the infrared-derived neon abundances are slightly higher than the optical values. This indicates either that 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.