Results of many years of theoretical and experimental studies of conditions to be met in order to obtain heavy-duty materials, particularly fibres and whiskers, were presented. Independent methods for the determination of theoretical and limited attainable strength, developed by the author, as well as two new indices (intermolecular and interatomic energy density) enabling to forecast mechanical properties, were discussed. Questions concerning maximal values of mechanical and thermal properties as well as the nature of elements of periodic table and their compounds having these properties were answered in the paper.