The amino acid l-α-alanine and its associated radiation-induced radicals display particular characteristics in solid-state that make it very appropriate for use in Electron Paramagnetic Resonance (EPR) dosimetry. In contrast to the number of experimental studies, relatively few theoretical studies have been published concerning the EPR parameters of these radicals. However, these studies inadequately account for the molecular environment of the alanine radicals in the crystalline lattice. Here, we present Density Functional Theory (DFT) calculations on one of the stable radiation-induced radicals of l-α-alanine both in molecular cluster models and in periodic models. An extensive investigation is presented on the various geometrical ingredients which have a substantial impact on the hyperfine coupling constants as the planarity of the radical backbone and the internal rotations of the final methyl and amino group vary. It is found that the accurate modeling of the hydrogen bonds with neighboring molecules is of utmost importance for an adequate reproduction of the experimental data.