Terahertz spectra of four alanine-rich peptides with known secondary structures were studied by terahertz time domain spectroscopy (THz-TDS) and by Fourier transform infrared spectroscopy (FTIR) using a synchrotron light source and a liquid-helium cooled bolometer. At ambient temperatures the usable bandwidth was restricted to 0.2-1.5 THz by the absorbance of water. The existence of a solvation shell around the peptide in solution was observed and its size estimated to be between 11 and 17 Å. By cooling the peptide solution to 80 K in order to reduce the water absorbance the bandwidth was increased to 0.1-3.0 THz for both THz-TDS and FTIR. Spectra were consistent with monotonic absorbance of the peptide and the existence of a solid amorphous low density solvation shell.