Identification of potentially amyloidogenic regions in polypeptide chains is very important because the amyloid fibril formation can be induced in most normal proteins. In our work we suggest a new method to detect amyloidogenic regions in protein sequence. It is based on the assumption that packing is tight inside an amyloid and therefore regions which could potentially pack well would have a tendency to form amyloids. This means that the regions with strong expected packing of residues would be responsible for the amyloid formation. We use this property to identify potentially amyloidogenic regions in proteins basing on their amino acid sequences only. Our predictions are consistent with known disease-related amyloidogenic regions for 8 of 11 amyloid-forming proteins and peptides in which the positions of amyloidogenic regions have been revealed experimentally. Predictions of the regions which are responsible for the formation of amyloid fibrils in proteins unrelated to disease have been also done.