Here we report the first in situ high-pressure study of sodium amide (NaNH2) as an agent in potential hydrogen storage applications by using combined Raman and infrared (IR) spectroscopies at room temperature and pressures up to similar to 16 GPa. Starting with an orthorhombic crystal structure at ambient pressure, sodium amide was found to transform to two new phases upon compression as evidenced by the changes in the characteristic Raman and IR modes as well as by examining the pressure dependences of these modes. Raman and IR measurements on NaNH2 collectively provided consistent information about the structural evolutions of NaNH2 under compression. Upon decompression, all Raman and IR modes were completely recovered, indicating the reversibility of the pressure-induced transformations in the entire pressure region. The combined Raman and IR spectroscopic data together allowed for the analysis of possible structures of the new high-pressure phases of NaNH2.