Inelastic incoherent neutron scattering (IINS) spectra were obtained at 10K for normal and deuterated l-cysteine. Raman and infrared spectra were also recorded. Geometry of l-cysteine molecule was optimized for the zwitterion form using ab initio HF/6-31G* level. The theoretical frequencies of normal and d(4)-l-cysteine were compared with INS, Raman and IR spectra. Normal coordinate analysis and band assignments based on ab initio calculations and experimental data are presented.