We present the results of density functional calculations of H-1,C-13, and N-14 hyperfine coupling constants (hfcc's) in radicals derived from the simple amino acid L-alanine. The calculations are performed using the B3LYP functional in combination with Pople basis sets (6-31G(d) and 6-311G(d)) and the IGLO-III basis set. Both isotropic and anisotropic hfcc's show good agreement with available experimental data. Detailed study of the isotropic hfcc's allows for investigation of specific geometrical features of the various radical structures. The scope and limitations of this type of calculations both for elucidation of experimental electron paramagnetic resonance spectra and investigation of radical structure are briefly discussed.