We present terahertz (THz) measurements and density functional theory (DFT) calculations of two amino acid crystals: DL-norleucine and DL-methionine. Their molecular structures are very similar and therefore also their crystal structures. We report the absorption spectra for both amino acids, which have a strong resonance at 1.87 THz in DL-norleucine and 1.94 THz in DL-methionine. In addition, we find a higher frequency resonance at 2.49 THz in DL-methionine, which has no corresponding mode in DL-norleucine. The experimental data are supported by DFT calculations, which show that the origin of the two strongest vibrational modes in DL-norleucine and DL-methionine are based on the same underlying vibrational motions, whereas the 2.49 THz resonance in DL-methionine is due to the motion of the sulfur atom, which is not present in DL-norleucine.